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arXiv · 1710.08226

Large subgroups in finite groups

Stefanos Aivazidis·Thomas W. Müller
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Abstract

Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if $C_G(N) \leq N$, so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing large subgroups in finite groups (see Theorems A and C). We also consider the more specialised problems of finding large (non-abelian) nilpotent as well as abelian subgroups in soluble groups.

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Stefanos Aivazidis, Thomas W. Müller. 2017-10-23. Large subgroups in finite groups. https://doi.org/10.1016/j.crma.2018.01.020

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