Brauer–Fowler theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-31

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Brauer%E2%80%93Fowler_theorem





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SUMMARY
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In mathematical finite group theory, the Brauer–Fowler theorem, proved by Brauer & Fowler (1955), states that if a group G has even order g  2 then it has a proper subgroup of order greater than g1/3. The technique of the proof is to count involutions (elements of order 2) in G. Perhaps more important is another result that the authors derive from the same count of involutions, namely that
up to isomorphism there are only a finite number of finite simple groups with a given centralizer of an involution. This suggested that finite simple groups could be classified by studying their centralizers of involutions, and it led to the discovery of several sporadic groups. Later it motivated a part of the classification of finite simple groups.