Powers of conjugacy classes in a finite group
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The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability concerning the case in which the power of a conjugacy class is a union of one or two conjugacy classes. Moreover, we show that the above conditions can be determined through the character table of the group.
KeywordsFinite groups Conjugacy classes Solvability Power of conjugacy classes Characters
Mathematics Subject Classification20E45 20D15 20C20
Part of this paper was written during the stay of C. Melchor at the University of Cambridge in autumn 2017, which was financially supported by the grant E-2017-02, Universitat Jaume I of Castellón. C. Melchor would like to thank R. Camina and the Department of Mathematics for their warm hospitality. A. Beltrán, M.J. Felipe and C. Melchor are supported by Proyecto PGC2018-096872-B-100, Ministerio de Ciencia, Innovación y Universidades.
- 5.The GAP Group, GAP—Groups, Algorithms and Programming, Vers. 4.7.7; (2015). (http://www.gap-system.org)