Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Varieties attached to an $ {\rm SL}\sb 2(2\sp k)$-module

Author: Geoffrey Mason
Journal: Proc. Amer. Math. Soc. 116 (1992), 343-350
MSC: Primary 20G05; Secondary 14M99
MathSciNet review: 1100661
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {G_k} = \operatorname{SL}_2({2^k})$ and $ V$ be an $ F{G_k}$-module with $ F$ a field containing $ \operatorname{GF}(2^k)$. We show that $ V$ is irreducible if and only if there is a subgroup $ {U_0}$ contained in a $ 2$-Sylow of $ {G_k}$ such that $ V$ affords the regular representation of $ {U_0}$. We further show how to construct a variety, defined over an algebraic closure of $ \operatorname{GF}(2)$, whose $ \operatorname{GF}(2^k)$-rational points parameterize those conjugacy classes of subgroups of $ {G_k}$, isomorphic to $ {U_0}$, that are not represented regularly on $ V$.

References [Enhancements On Off] (What's this?)

  • [1] J. Alperin, Projective methods for $ \operatorname{SL}(2,2^n)$, J. Pure Appl. Algebra 15 (1979), 219-234. MR 537496 (80e:20012)
  • [2] J. F. Carlson, Varieties for modules, Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987. MR 933347 (89b:20032)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20G05, 14M99

Retrieve articles in all journals with MSC: 20G05, 14M99

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society