Hokkaido Mathematical Journal

Finite groups with some nonnormal subgroups of non-prime-power order

Jiangtao SHI, Cui ZHANG, and Dengfeng LIANG

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Abstract

We prove that a group G with exactly three classes of nonnormal proper subgroups of the same non-prime-power order is nonsolvable if and only if GA5, and a group G with exactly four classes of nonnormal proper subgroups of the same non-prime-power order is nonsolvable if and only if GPSL(2,7) or PSL(2,8). Moreover, we prove that any group G with at most nine classes of nonnormal nontrivial subgroups of the same order is always solvable except for GA5, PSL2(7) or SL2(5).

Article information

Source
Hokkaido Math. J., Volume 44, Number 3 (2015), 387-396.

Dates
First available in Project Euclid: 1 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1470053370

Digital Object Identifier
doi:10.14492/hokmj/1470053370

Mathematical Reviews number (MathSciNet)
MR3532115

Zentralblatt MATH identifier
1343.20020

Subjects
Primary: 20D05: Finite simple groups and their classification 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks [See also 20F17]

Keywords
nonsolvable group class of the same order nonnormal non-prime-power order

Citation

SHI, Jiangtao; ZHANG, Cui; LIANG, Dengfeng. Finite groups with some nonnormal subgroups of non-prime-power order. Hokkaido Math. J. 44 (2015), no. 3, 387--396. doi:10.14492/hokmj/1470053370. https://projecteuclid.org/euclid.hokmj/1470053370


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