The Development of the Theory of $p$-Groups
Paul Hill
Source: Rocky Mountain J. Math. Volume 32, Number 4
(2002), 1135-1151.
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Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1181070013
Digital Object Identifier: doi:10.1216/rmjm/1181070013
Mathematical Reviews number (MathSciNet): MR1987598
Zentralblatt MATH identifier: 1034.20046
References
P. Cawley and A. Hales, The structure of abelian $p$-groups given by certain presentations, J. Algebra 12 (1969), 10-23.
Mathematical Reviews (MathSciNet): MR238947
Digital Object Identifier: doi:10.1016/0021-8693(69)90014-3
--------, The structure of abelian $p$-groups given by certain presentations, J. Algebra 18 (1971), 264-268.
Mathematical Reviews (MathSciNet): MR276329
Zentralblatt MATH: 0219.20034
Digital Object Identifier: doi:10.1016/0021-8693(71)90059-7
D. Cutler, Abelian $p$-groups determined by their $p^n$-socles, Conf. on Abelian Group Theory (Oberwolfach, 1985), Gordon & Breach, New York, 1987, pp. 111-116.
Mathematical Reviews (MathSciNet): MR1011307
Zentralblatt MATH: 0654.20062
D. Cutler, A. Mader and C. Megibben, Essentially indecomposable abelian $p$-groups having a filtration of prescribed type, Abelian Group Theory, Contemp. Math. 87, Amer. Math. Soc., Providence, pp. 43-50.
Mathematical Reviews (MathSciNet): MR995263
Zentralblatt MATH: 0679.20046
M. Dugas and R. Vergohsen, On socles of Abelian $p$-groups in $L$, Rocky Mountain J. Math. 18 1988, 733-752.
Mathematical Reviews (MathSciNet): MR1002172
Digital Object Identifier: doi:10.1216/RMJ-1988-18-4-733
Project Euclid: euclid.rmjm/1250126049
Zentralblatt MATH: 0693.20050
P. Eklof and M. Huber, On $\o$-filtered vector spaces and their applications to abelian $p$-groups, Rocky Mountain J. Math. 18, 123-136.
Mathematical Reviews (MathSciNet): MR935730
Digital Object Identifier: doi:10.1216/RMJ-1988-18-1-123
Project Euclid: euclid.rmjm/1250126292
Zentralblatt MATH: 0652.20055
P. Eklof and A. Mekler, Almost free modules, North-Holland, Amsterdam, 1990.
Mathematical Reviews (MathSciNet): MR1055083
E. Enochs, Isomorphic refinements of decompositions of a primary group into closed groups, Bull. Soc. Math. France 91 (1963), 63-75.
Mathematical Reviews (MathSciNet): MR150197
Zentralblatt MATH: 0118.03703
L. Fuchs, Abelian groups, Publ. House of the Hungar. Acad. Sci., Budapest, 1958.
Mathematical Reviews (MathSciNet): MR106942
--------, Infinite abelian groups, Vol. 1 and 2, Academic Press, New York, 1970, 1973.
--------, Valuated vector spaces, J. Algebra 35 (1975), 23-38.
Mathematical Reviews (MathSciNet): MR371995
Zentralblatt MATH: 0318.15002
Digital Object Identifier: doi:10.1016/0021-8693(75)90033-2
P. Griffith, Transitive and fuly transitive primary abelian groups, Pacific J. Math. 25 (1968), 249-254.
Mathematical Reviews (MathSciNet): MR230816
Zentralblatt MATH: 0157.05901
Project Euclid: euclid.pjm/1102986267
--------, Infinite abelian groups, Chicago Lectures in Math., Univ. of Chicago Press, 1970.
D.K. Harrison, Infinite abelian groups and homological methods, Ann. Math. 69 (1959), 366-391.
Mathematical Reviews (MathSciNet): MR104728
Digital Object Identifier: doi:10.2307/1970188
JSTOR: links.jstor.org
P. Hill, Certain pure subgroups of primary groups, Topics in Abelian Groups, Scott-Foresman and Co., Chicago, 1963, pp. 311-314.
Mathematical Reviews (MathSciNet): MR169908
--------, Pure subgroup having prescribed socles, Bull. Amer. Math. Soc. 71 (1965), 608-609.
Mathematical Reviews (MathSciNet): MR178066
Zentralblatt MATH: 0132.27205
Digital Object Identifier: doi:10.1090/S0002-9904-1965-11357-X
Project Euclid: euclid.bams/1183527226
--------, A classification of direct sums of closed groups, Acta Math. Acad. Sci. Hungar. 17 (1966), 263-266.
Mathematical Reviews (MathSciNet): MR199258
Zentralblatt MATH: 0144.26504
Digital Object Identifier: doi:10.1007/BF01894872
P. Hill, Sums of countable primary groups, Proc. Amer. Math. Soc. 17 (1966), 1469-1470.
Mathematical Reviews (MathSciNet): MR199259
Zentralblatt MATH: 0158.27405
Digital Object Identifier: doi:10.2307/2035766
JSTOR: links.jstor.org
--------, The isomorphic refinement theorem for direct sums of closed groups, Proc. Amer. Math. Soc. 18 (1967), 913-919.
Mathematical Reviews (MathSciNet): MR215919
Zentralblatt MATH: 0168.27302
Digital Object Identifier: doi:10.2307/2035138
JSTOR: links.jstor.org
--------, On the classification of abelian groups, photocopied manuscript, University of Houston, Texas, 1967.
--------, Extending automorphisms on primary groups, Bull. Amer. Math. Soc. 74 (1968), 1123-1124.
Mathematical Reviews (MathSciNet): MR233890
Zentralblatt MATH: 0192.35701
Digital Object Identifier: doi:10.1090/S0002-9904-1968-12072-5
Project Euclid: euclid.bams/1183530112
--------, On primary groups with uncountable many elements of infinite height, Arch. Math. 19 (1968), 279-283.
Mathematical Reviews (MathSciNet): MR228579
Digital Object Identifier: doi:10.1007/BF01899503
Zentralblatt MATH: 0203.32802
--------, Isotype subgroups of direct sums of countable groups, Illinois J. Math. 13 (1969), 281-290.
Mathematical Reviews (MathSciNet): MR240198
Zentralblatt MATH: 0177.04201
--------, Endomorphism rings generated by units, Trans. Amer. Math. Soc. 141 (1969), 99-105.
Mathematical Reviews (MathSciNet): MR242944
Digital Object Identifier: doi:10.2307/1995092
JSTOR: links.jstor.org
--------, On transitive and fully transitive primary groups, Proc. Amer. Math. Soc. 22 (1969), 414-417.
Zentralblatt MATH: 0192.35601
Mathematical Reviews (MathSciNet): MR269735
Digital Object Identifier: doi:10.2307/2037067
JSTOR: links.jstor.org
--------, A countability condition for primary groups presented by relations of length two, Bull. Amer. Math. Soc. 75 (1969), 780-782.
Mathematical Reviews (MathSciNet): MR246959
Digital Object Identifier: doi:10.1090/S0002-9904-1969-12287-1
Project Euclid: euclid.bams/1183530643
--------, Automorphisms of countable primary groups, Proc. Amer. Math. Soc. 25 (1970), 135-140.
Mathematical Reviews (MathSciNet): MR255674
Zentralblatt MATH: 0224.20047
Digital Object Identifier: doi:10.2307/2036541
JSTOR: links.jstor.org
--------, Countable unions of totally projective groups, Trans. Amer. Math. Soc. 190 (1974), 385-391.
Zentralblatt MATH: 0295.20058
Mathematical Reviews (MathSciNet): MR338212
Digital Object Identifier: doi:10.2307/1996971
--------, Isotype subgroups of totally projective groups, Abelian Group Theory, Lecture Notes in Math., vol. 874, Springer, New York, 1981, pp. 305-321.
Mathematical Reviews (MathSciNet): MR645937
Digital Object Identifier: doi:10.1007/BFb0090544
--------, Criteria for total projectivity, Canad. J. Math. 33 (1981), 817-825.
Zentralblatt MATH: 0432.20048
Mathematical Reviews (MathSciNet): MR634140
--------, The equivalent of high subgroups, Proc. Amer. Math. Soc. 88 (1983), 207-211.
Mathematical Reviews (MathSciNet): MR695242
Zentralblatt MATH: 0522.20038
Digital Object Identifier: doi:10.2307/2044700
JSTOR: links.jstor.org
--------, The classification of $N$-groups, Houston J. Math. 10 (1984), 43-55.
Mathematical Reviews (MathSciNet): MR736574
Zentralblatt MATH: 0545.20042
--------, On the structure of abelian $p$-groups, Trans. Amer. Math. Soc. 288 (1985), 505-525.
Mathematical Reviews (MathSciNet): MR776390
Zentralblatt MATH: 0573.20053
Digital Object Identifier: doi:10.2307/1999950
JSTOR: links.jstor.org
--------, Simultaneous decompositions of an abelian group and a subgroup, Quart. J. Math. Oxford 36 (1985), 425-433.
Zentralblatt MATH: 0584.20043
Mathematical Reviews (MathSciNet): MR816484
Digital Object Identifier: doi:10.1093/qmath/36.4.425
--------, Modular group algebras and simply presented groups, Abelian Groups and Modules, Birkhauser, 1999, pp. 7-22.
Mathematical Reviews (MathSciNet): MR1735555
Zentralblatt MATH: 0938.16022
P. Hill and C. Megibben, Minimal pure subgroups in primary groups, Bull. Soc. Math. France 92 (1964), 251-257.
Mathematical Reviews (MathSciNet): MR186731
Zentralblatt MATH: 0214.04103
--------, Quasi-closed primary groups, Acta Math. Acad. Sci. Hungar. 16 (1965), 271-274.
Zentralblatt MATH: 0209.33204
Mathematical Reviews (MathSciNet): MR191957
Digital Object Identifier: doi:10.1007/BF01904835
--------, On primary groups with countable basic subgroups, Trans. Amer. Math. Soc. 124 (1966), 49-59.
Zentralblatt MATH: 0146.04203
Mathematical Reviews (MathSciNet): MR199260
Digital Object Identifier: doi:10.2307/1994434
JSTOR: links.jstor.org
--------, Extending automorphisms and lifting decompositions in abelian groups, Studies on Abelian Groups, Paris, 1968.
Zentralblatt MATH: 0183.03202
--------, On the theory and classification of abelian $p$-groups, Math. Z. 190 (1985), 17-38.
Zentralblatt MATH: 0535.20031
Mathematical Reviews (MathSciNet): MR793345
Digital Object Identifier: doi:10.1007/BF01159160
--------, Subsocles supporting isotype and balanced subgroups, Canad. Math. Bull. 36 (1993), 419-425.
Zentralblatt MATH: 0801.20028
Mathematical Reviews (MathSciNet): MR1245315
P. Hill and W. Ullery, On commutative group algebras of mixed groups, Comm. Algebra 25 (1997), 4029-4038.
Mathematical Reviews (MathSciNet): MR1481586
Zentralblatt MATH: 0901.16012
Digital Object Identifier: doi:10.1080/00927879708826107
R. Hunter, F. Richman and E. Walker, Ulm's theorem for simply presented valuated $p$-groups, Conf. on Abelian Group Theory (Oberwolfack, 1985), Gordon and Breach, New York, 1987, pp. 33-64.
Mathematical Reviews (MathSciNet): MR1011304
Zentralblatt MATH: 0661.20035
J. Irwin, High subgroups of abelian torsion groups, Pacific J. Math. 11 (1961), 1375-1384.
Mathematical Reviews (MathSciNet): MR136654
Zentralblatt MATH: 0106.02303
Project Euclid: euclid.pjm/1103036920
J. Irwin and E. Walker, On $N$-high subgroups of abelian groups, Pacific J. Math. 11 (1961), 1363-1374.
Mathematical Reviews (MathSciNet): MR136653
Zentralblatt MATH: 0106.02304
Project Euclid: euclid.pjm/1103036919
I. Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954.
Mathematical Reviews (MathSciNet): MR65561
I. Kaplansky and G. Mackey, A generalization of Ulm's theorem, Summa Brazil. Math. 2 (1951), 195-202.
Mathematical Reviews (MathSciNet): MR49165
Zentralblatt MATH: 0054.01803
P. Keef, On set theory and the balanced-projective dimension of $C_\Omega$-groups, Contemp. Math. 89, Amer. Math. Soc., 1989, pp. 31-41.
Mathematical Reviews (MathSciNet): MR995262
Zentralblatt MATH: 0673.20031
--------, Abelian groups and the torsion product, Conf. on Abelian Groups and Modules (Colorado Springs, 1995), Lecture Notes in Pure and Appl. Math. 182, Dekker, New York, 1966, pp. 45-66.
Mathematical Reviews (MathSciNet): MR1415622
Zentralblatt MATH: 0888.20034
G. Kolettis, Direct sums of countable groups, Duke Math. J. 27 (1960), 111-125.
Mathematical Reviews (MathSciNet): MR110748
Zentralblatt MATH: 0091.02802
Digital Object Identifier: doi:10.1215/S0012-7094-60-02711-3
Project Euclid: euclid.dmj/1077468922
S. MacLane, Homology, Academic Press, New York, 1963.
Mathematical Reviews (MathSciNet): MR156879
C. Megibben, Large subgroups and small homomorphisms, Michigan Math. J. 13 (1966), 134-144.
Mathematical Reviews (MathSciNet): MR195939
Digital Object Identifier: doi:10.1307/mmj/1028999539
Project Euclid: euclid.mmj/1028999539
--------, A nontransitive, fully transitive primary abelian group, J. Algebra 13 (1969), 571-574.
Mathematical Reviews (MathSciNet): MR262362
Zentralblatt MATH: 0208.03501
Digital Object Identifier: doi:10.1016/0021-8693(69)90118-5
--------, Crawley's problem on the unique $\o$-elongation of $p$-groups is undecidable, Pacific J. Math. 107 (1983), 205-212.
Zentralblatt MATH: 0521.20035
Mathematical Reviews (MathSciNet): MR701817
Project Euclid: euclid.pjm/1102720748
--------, $\o_1$-separable $p$-groups, Conf. on Abelian Group Theory (Oberwolfach, 1985), Gordon and Breach, New York, 1987, pp. 117-136.
Mathematical Reviews (MathSciNet): MR1011308
R. Nunke, On the structure of Tor, Proc. Colloq. Abelian Groups, Budapest, 1964, 115-124.
Mathematical Reviews (MathSciNet): MR169912
--------, Homology and direct sums of countable abelian groups, Math. Z. 101 (1967), 182-212.
Zentralblatt MATH: 0173.02401
Mathematical Reviews (MathSciNet): MR218452
Digital Object Identifier: doi:10.1007/BF01135839
L.D. Parker and E.A. Walker, An extension of the Ulm-Kolettis theorems, Studies on Abelian Groups, Paris, 1968, pp. 309-325.
Mathematical Reviews (MathSciNet): MR265458
Zentralblatt MATH: 0182.04104
R.S. Pierce, Homomorphisms of primary abelian groups, Topics in Abelian Groups, Scott-Foresman, Chicago, 1963, pp. 215-310.
Mathematical Reviews (MathSciNet): MR177035
F. Richman and E. Walker, Extending Ulm's theorem without group theory, Proc. Amer. Math. Soc. 21 (1969), 194-196.
Mathematical Reviews (MathSciNet): MR240201
Zentralblatt MATH: 0172.03202
Digital Object Identifier: doi:10.2307/2036891
JSTOR: links.jstor.org
L. Rogers, Ulm's theorem for partially ordered structures related to simply presented $p$-groups, Trans. Amer. Math. Soc. 227 (1977), 333-343.
Mathematical Reviews (MathSciNet): MR442115
Zentralblatt MATH: 0357.20032
Digital Object Identifier: doi:10.2307/1997464
JSTOR: links.jstor.org
H. Ulm, Zur theorie der abzählbar-unendlichen abelschen Gruppen, Math. Ann. 107 (1993), 774-803.
R. Warfield, A classification theorem for abelian $p$-groups, Trans. Amer. Math. Soc. 210 (1975), 149-168.
Mathematical Reviews (MathSciNet): MR372071
Zentralblatt MATH: 0324.20058
Digital Object Identifier: doi:10.2307/1997128
L. Zippin, Countable torsion groups, Ann. Math. 36 (1935), 86-99.
Mathematical Reviews (MathSciNet): MR1503210
Digital Object Identifier: doi:10.2307/1968666
JSTOR: links.jstor.org
Rocky Mountain Journal of Mathematics