Quasisimple classical groups and their complex group algebras
Let H be a finite quasisimple classical group, i.e., H is perfect and S:= H/Z(H) is a finite simple classical group. We prove that, excluding the open cases when S has a very exceptional Schur multiplier such as PSL3(4) or PSU4(3), H is uniquely determined by the structure of its complex group algebra. The proofs make essential use of the classification of finite simple groups as well as the results on prime power character degrees and relatively small character degrees of quasisimple classical groups.
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- [Brau]R. Brauer, Representations of finite groups, in Lectures on Modern Mathematics, Vol. I, Wiley, New York, 1963, pp. 133–175.Google Scholar
- [GAP]The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.4.12, 2008, http://www.gap-system.org.
- [Lub]F. Lübeck, Data for finite groups of Lie type and related algebraic groups, http://www.math.rwth-aachen.de/~Frank.Luebeck/chev/index.html
- [MaK]V. D. Mazurov and E. I. Khukhro, Unsolved Problems in Group Theory, the Kourovka Notebook, 17th edition, Novosibirsk, 2010.Google Scholar