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Title of Journal: Arch Math

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Abbravation: Archiv der Mathematik

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Springer Basel

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DOI

10.1007/s11434-013-0043-2

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1420-8938

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Lower bounds on the number of maximal subgroups in

Authors: L K Lauderdale
Publish Date: 2013/07/03
Volume: 101, Issue: 1, Pages: 9-15
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Abstract

For a finite group G let mG denote the set of maximal subgroups of G and πG denote the set of primes which divide G When G is a cyclic group an elementary calculation proves that mG = πG In this paper we prove lower bounds on mG when G is not cyclic In general mG geq piG+p where p in piG is the smallest prime that divides G If G has a noncyclic Sylow subgroup and q in piG is the smallest prime such that Q in rm syl qG is noncyclic then mG geq piG+q Both lower bounds are best possible

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