Geodesic
Periodic groups saturated with finite Frobenius groups with complements of orders divisible by a prime number
Algebra i logika, Tome 62 (2023) no. 6, pp. 701-707

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A finite Frobenius group in which the order of complements is divisible by a prime number $p$ is called a $\text{Р¤}_{ p}$-group. We prove that the following theorem holds. THEOREM. Let $G$ be a periodic group with a finite element $a$ of prime order $p>2$ saturated with ${\Phi}_{ p}$-groups. Then $G=F\leftthreetimes H$ is a Frobenius group with kernel $F$ and complement $H$. If $G$ contains an involution $i$ commuting with the element $a$, then $H=C_G(i)$ and $F$ is Abelian, and $H=N_G(\langle a\rangle)$ otherwise.
Keywords: periodic group, finite Frobenius group
Mots-clés : $\text{Р¤}_{ p}$-group. 
@article{AL_2023_62_6_a0,
     author = {B. E. Durakov},
     title = {Periodic groups saturated with finite {Frobenius} groups with complements of orders divisible by a prime number},
     journal = {Algebra i logika},
     pages = {701--707},
     publisher = {mathdoc},
     volume = {62},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_6_a0/}
}
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B. E. Durakov. Periodic groups saturated with finite Frobenius groups with complements of orders divisible by a prime number. Algebra i logika, Tome 62 (2023) no. 6, pp. 701-707. http://geodesic.mathdoc.fr/item/AL_2023_62_6_a0/