Shane Cernele, Masoud Kamgarpour, and Zinovy Reichstein: Maximal representation dimension for groups of order p^n,,

Submission: 2009, Nov 4

The representation dimension rdim(G) of a finite group G is the smallest positive integer m for which there exists an embedding of G in GL_m(C). In this paper we find the largest value of rdim(G), as G ranges over all groups of order p^n, for a fixed prime p and a fixed exponent n.

2000 Mathematics Subject Classification: 20C15, 20D15

Keywords and Phrases: $p$-group, representation dimension, symplectic subspace, generalized Heisenberg group

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