Given a finite group G, consider the prime graph built on the set of conjugacy class sizes of G. Denoting by π0 the set of vertices of this graph that are not adjacent to at least one other vertex, we show that the Hall π0 -subgroups of G (which do exist) are metabelian.
Incomplete vertices in the prime graph on conjugacy class sizes of finite groups / C. Casolo; S. Dolfi; E. Pacifici; L. Sanus. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 376:(2013), pp. 46-57. [10.1016/j.jalgebra.2012.10.012]
Incomplete vertices in the prime graph on conjugacy class sizes of finite groups
CASOLO, CARLO;DOLFI, SILVIO;E. Pacifici;
2013
Abstract
Given a finite group G, consider the prime graph built on the set of conjugacy class sizes of G. Denoting by π0 the set of vertices of this graph that are not adjacent to at least one other vertex, we show that the Hall π0 -subgroups of G (which do exist) are metabelian.
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