Revista Matemática Iberoamericana

On some permutable products of supersoluble groups

Manuel J. Alejandre, A. Ballester-Bolinches, John Cossey, and M. C. Pedraza-Aguilera

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Abstract

It is well known that a group $G = AB$ which is the product of two supersoluble subgroups $A$ and $B$ is not supersoluble in general. Under suitable permutability conditions on $A$ and $B$, we show that for any minimal normal subgroup $N$ both $AN$ and $BN$ are supersoluble. We then exploit this to establish some sufficient conditions for $G$ to be supersoluble.

Article information

Source
Rev. Mat. Iberoamericana, Volume 20, Number 2 (2004), 413-425.

Dates
First available in Project Euclid: 17 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1087482021

Mathematical Reviews number (MathSciNet)
MR2073126

Zentralblatt MATH identifier
1063.20024

Subjects
Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks [See also 20F17] 20D35: Subnormal subgroups 20D40: Products of subgroups

Keywords
finite groups products subnormality supersolubility

Citation

Alejandre, Manuel J.; Ballester-Bolinches, A.; Cossey, John; Pedraza-Aguilera, M. C. On some permutable products of supersoluble groups. Rev. Mat. Iberoamericana 20 (2004), no. 2, 413--425. https://projecteuclid.org/euclid.rmi/1087482021


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References

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