Large subgroups in finite groups |
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| Authors: | Stefanos Aivazidis Thomas W Müller |
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| Institution: | 1. Einstein Institute of Mathematics, Edmond J. Safra Campus, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 9190401, Israel;2. School of Mathematical Sciences, Queen Mary & Westfield College, University of London, Mile End Road, London E1 4NS, United Kingdom |
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| Abstract: | Following Isaacs (see 6, p. 94]), we call a normal subgroup N of a finite group Glarge, if , 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 Theorem A, Theorem 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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