Vol. 36, No. 2, 1971

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On the conjugating representation of a finite group

Richard Lewis Roth

Vol. 36 (1971), No. 2, 515–521

A natural permutation representation for any finite group is the conjugating representation T: for each g G, T(g) is the permutation on the set {xx G} given by T(g)(x) = gxg1. Frame, Solomon and Gamba have studied some of its properties. This paper considers the question of which complex irreducible representations occur as components of T, in particular the conjecture that any such representation whose kernel contains the center of G is a component of T. This conjecture is verified for a few special cases and a number of related results are obtained, especially with respect to the one-dimensional components of T.

Mathematical Subject Classification
Primary: 20.80
Received: 11 May 1970
Published: 1 February 1971
Richard Lewis Roth