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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor
Prime power indices in factorised groups.
Mediterr. J. Math., 14(6):Art. 225, 15, 2017
Let the group G=AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in A∪B have prime power indices in G, for some prime p. More generally, we also consider the case that all prime power order elements in A∪B have prime power indices in G. In particular, when G=A=B, we obtain as a consequence some known results.
2010 Mathematics Subject Classification: 20D10, 20D40, 20E45, 20D20
Keywords: Finite groups, Products of groups, Conjugacy classes, Sylow subgroups