We determine the structure of a finite group G whose noncentral real conjugacy classes have prime size. In particular, we show that G is solvable and that the set of the sizes of its real classes is one of the following: {1},{1, 2}, {1, p}, or {1, 2, p}, where p is an odd prime.
Finite groups with real conjugacy classes of prime size / S. Dolfi, E. Pacifici, L. Sanus. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 175:1(2010), pp. 179-189. [10.1007/s11856-010-0008-y]
Finite groups with real conjugacy classes of prime size
E. PacificiSecondo
;
2010
Abstract
We determine the structure of a finite group G whose noncentral real conjugacy classes have prime size. In particular, we show that G is solvable and that the set of the sizes of its real classes is one of the following: {1},{1, 2}, {1, p}, or {1, 2, p}, where p is an odd prime.
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