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- W2114886360 abstract "Publisher Summary Great progress has been made recently in the problem of classifying those finite simple groups in which the centralizer of some involution is not 2-constrained. Part of the reason for this is a recent theorem of Aschbacher that gives a normal form for the centralizer of an involution in a large class of such groups. However, in a group in which the centralizers of all involutions are 2-constrained, no such canonical form is anticipated. Accordingly, in these circumstances, it seems to be appropriate to study instead the centralizers of elements of order three. This chapter discusses one of the simplest cases in which the element of order three has a non-3-constrained centralizer, and presents the theorem, as per which if G be a finite simple group and a be an element of G of order 3, and if the group C G (a)/ is isomorphic to one of the groups PSL(2,q), PGL(2,q), or P∑L (2,q), where q is the power of an odd prime. Suppose in addition there is a subgroup P of G, where P is an elementary abelian group of order 3 2 and all nonidentity elements of P are conjugate to the element a . Then, G is isomorphic to one of the following groups: (1) PSU(3,5), (2) PSL(3,7), (3) M 22, (4) M 23, (5) M 24, (6) HS, the Higman–Sims group, (7) R, the Rudvalis group." @default.
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- W2114886360 date "1977-09-01" @default.
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- W2114886360 title "Some characterizations by centralizers of elements of order 3" @default.
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- W2114886360 doi "https://doi.org/10.1016/0021-8693(77)90297-6" @default.
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