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- W4200520245 abstract "Let x be an element of a finite group G, and p a prime factor of the order of G. It is clear that there always exists a unique minimal subnormal subgroup containing x, say [Formula: see text]. We call the conjugacy class of x in [Formula: see text] the sub-class of x in G, see [G. Qian and Y. Yang, On sub-class sizes of finite groups, J. Aust. Math. Soc. (2020) 402–411]. In this paper, assume that [Formula: see text] is the product of the subgroups A and B, we investigate the solvability, p-nilpotence and supersolvability of the group G under the condition that the sub-class sizes of prime power order elements in [Formula: see text] are [Formula: see text] free, [Formula: see text] free and square free, respectively, so that some known results relevant to conjugacy class sizes are generalized." @default.
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- W4200520245 date "2021-12-23" @default.
- W4200520245 modified "2023-09-28" @default.
- W4200520245 title "The sub-class sizes of some elements being square free" @default.
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- W4200520245 doi "https://doi.org/10.1142/s0219498823500743" @default.
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