University of Birmingham > Talks@bham > Algebra Seminar > large centralizers in finite groups.

large centralizers in finite groups.

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We discuss recent joint work with Bob Guralnick, partly inspired by the famous Brauer-Fowler paper of 1956. We prove a number of results ( some using the classification of finite simple groups (CFSG), some not) which bound the index of the Fitting subgroup of a finite group G in terms of centralizers of certain elements of G, especially involutions. We also provide a CFSG -free bound on the maximum dimension of the fixed-point space of an involution in a finite linear group.

This talk is part of the Algebra Seminar series.

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