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Finite Groups Admitting ap-Solvable Operator Group

✍ Scribed by Yanming Wang

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 113 KB
Volume: 204
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7351

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✦ Synopsis

Let G be a finite group and H be an operator group of G. Suppose that

that G is solvable, if H acts non-trivially on G but acts trivially on all proper H-invariant subgroups in an appropriately chosen class subgroups. The detailed structure of such a group G is determined.

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In this paper G denotes a finite group. As is well known, the converse of Lagrange's theorem in group theory does not hold. That is, given a finite group G of order n, and given a divisor d of n, G need not have a subgroup of order d. Indeed, a celebrated theorem of P. Hall states that it suffices t