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The modular representation algebra of groups with Sylow 2-subgroup Z2 × Z2

Published online by Cambridge University Press:  09 April 2009

S. B. Conlon
S. B. Conlon
Affiliation:
University of Sydney
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Let k be a field of characteristic 2 and let G be a finite group. Let A(G) be the modular representation algebra1 over the complex numbers C, formed from kG-modules2. If the Sylow 2-subgroup of G is isomorphic to Z2×Z2, we show that A(G) is semisimple. We make use of the theorems proved by Green [4] and the results of the author concerning A(4) [2], where 4 is the alternating group on 4 symbols.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1966 , pp. 76 - 88
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Conlon, S. B., Twisted group algebras and their representations, J. Austral. Math. Soc. 4 (1964), 152–173.CrossRefGoogle Scholar
[2]Conlon, S. B., Certain representation algebras, J. Austral. Math. Soc. 5 (1965), 83–99.CrossRefGoogle Scholar
[3]Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras, Interscience, New York, 1962.Google Scholar
[4]Green, J. A., A transfer theorem for modular representations, J. of Algebra 1 (1964), 73–84.CrossRefGoogle Scholar
[5]Higman, D. G., Indecomposable representations at characteristic p, Duke Math. J. 21 (1954), 377–381.CrossRefGoogle Scholar