Bender groups as standard subgroups

Authors:
Robert L. Griess, David R. Mason and Gary M. Seitz

Journal:
Trans. Amer. Math. Soc. **238** (1978), 179-211

MSC:
Primary 20D05

MathSciNet review:
0466300

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Abstract: A subgroup *X* of a finite group *G* is called -*standard* if is quasisimple, is tightly embedded in *G* and . This generalizes the notion of standard subgroups.

Theorem. *Let G be a finite group with* . *Suppose X is* -*standard in G and* *or* . *Assume* . *Then* *and one of the following holds*:

.

*and* .

*and* .

*and* .

*and* .

*and* (*the Rudvalis group*).

*and* .

*and G has sectional* 2-*rank at most* 4.

*In particular, if G is simple*, .

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0466300-7

Article copyright:
© Copyright 1978
American Mathematical Society