Attila Maróti
Bounding the number of conjugacy classes of a permutation group
For a finite group G, let k(G) denote the number of conjugacy classes of G. If G is a finite permutation group of degree n > 2, then k(G) ? 3(n?1)/2. This is an extension of a theorem of Kovács and Robinson and in turn of Riese and Schmid. If N is a normal subgroup of a completely reducible subgroup of GL(n, q), then k(N ) ? q5n. Similarly, if N is a normal subgroup of a primitive subgroup of Sn, then k (N ) ? p (n) where p (n) is the number of partitions of n. These bounds improve results of Liebeck and Pyber.
Journal of Group Theory, Walter de Gruyter
Print ISSN: 1433-5883
Volume: 8, 05/2005
Pages: 273 - 289
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