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Abelian p-subgroups of the general linear group

Published online by Cambridge University Press:  09 April 2009

J. T. Goozeff
J. T. Goozeff
Affiliation:
Wollongong University CollegeWollongong, N.S.W.
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A. J. Weir [1] has found the maximal normal abelian subgroups of the Sylow p-subgroups of the general linear group over a finite field of characteristic p, and a theorem of J. L. Alperin [2] shows that the Sylow p-subgroups of the general linear group over finite fields of characteristic different from p have a unique largest normal abelian subgroup and that no other abelian subgroup has order as great.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 3 , August 1970 , pp. 257 - 259
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Weir, A. J., Sylow p-subgroups of the general linear group over finite fields of characteristic, p. Proc. Amer. Math. Soc. 6 (1955) 454–464.Google Scholar
[2]Alperin, J. I., Large abelian subgroups of p-groups, Trans. Amer. Math. Soc. 117 (1965), 10–20.Google Scholar