Let G be a finite group acting faithfully on a finite vector space M in such a way that the centralizer of every element of M contains a Sylow q-subgroup of G as a central subgroup (for a fixed prime divisor q of |G| with (q, |M|) 1). Then G is isomorphic to a subgroup of the semi-linear group on M.
Some linear actions of finite groups with q′-orbits / C.Casolo. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - STAMPA. - 13:(2010), pp. 503-534. [10.1515/JGT.2010.003]
Some linear actions of finite groups with q′-orbits
CASOLO, CARLO
2010
Abstract
Let G be a finite group acting faithfully on a finite vector space M in such a way that the centralizer of every element of M contains a Sylow q-subgroup of G as a central subgroup (for a fixed prime divisor q of |G| with (q, |M|) 1). Then G is isomorphic to a subgroup of the semi-linear group on M.
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