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- W4221150366 abstract "We consider a finite group $G$ with a normal subgroup $N$ so that all elements of $G setminus N$ have prime power order. We prove that if there is a prime $p$ so that all the elements in $G setminus N$ have $p$-power order, then either $G$ is a $p$-group or $G = PN$ where $P$ is a Sylow $p$-subgroup and $(G,P,P cap N)$ is a Frobenius-Wielandt triple. We also prove that if all the elements of $G setminus N$ have prime power orders and the orders are divisible by two primes $p$ and $q$, then $G$ is a ${ p, q }$-group and $G/N$ is either a Frobenius group or a $2$-Frobenius group. If all the elements of $G setminus N$ have prime power orders and the orders are divisible by at least three primes, then all elements of $G$ have prime power order and $G/N$ is nonsolvable." @default.
- W4221150366 created "2022-04-03" @default.
- W4221150366 creator A5006684067 @default.
- W4221150366 date "2022-03-04" @default.
- W4221150366 modified "2023-09-23" @default.
- W4221150366 title "Groups having all elements off a normal subgroup with prime power order" @default.
- W4221150366 doi "https://doi.org/10.48550/arxiv.2203.02537" @default.
- W4221150366 hasPublicationYear "2022" @default.
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