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- W4313303637 abstract "In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions strongly affect the group structure. In particular, for every prime $p$, we prove a sufficient condition for a finite group to be $p$-nilpotent, that is, a group whose elements of $p'$-order form a normal subgroup. Moreover, we characterize finite cyclic groups with prescribed number of prime divisors." @default.
- W4313303637 created "2023-01-06" @default.
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- W4313303637 date "2022-12-28" @default.
- W4313303637 modified "2023-09-24" @default.
- W4313303637 title "On the structure of finite groups determined by the arithmetic and geometric means of element orders" @default.
- W4313303637 doi "https://doi.org/10.48550/arxiv.2212.13770" @default.
- W4313303637 hasPublicationYear "2022" @default.
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