In mathematicalfinite group theory, the Brauer–Fowler theorem, proved by Brauer & Fowler (1955), states that if a group G has even orderg > 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.
brauer, fowler, theorem, mathematical, finite, group, theory, proved, brauer, fowler, 1955, states, that, group, even, order, then, proper, subgroup, order, greater, than, technique, proof, count, involutions, elements, order, perhaps, more, important, another. In mathematical finite group theory the Brauer Fowler theorem proved by Brauer amp Fowler 1955 states that if a group G has even order g gt 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 References editBrauer R Fowler K A 1955 On groups of even order Annals of Mathematics Second Series 62 3 565 583 doi 10 2307 1970080 ISSN 0003 486X JSTOR 1970080 MR 0074414 nbsp This abstract algebra related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Brauer Fowler theorem amp oldid 1058075420, wikipedia, wiki, book, books, library,
