Geodesic
Groups saturated with finite Frobenius groups with complements of even order
Algebra i logika, Tome 60 (2021) no. 6, pp. 569-574

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We prove a theorem stating the following. Let $G$ be a periodic group saturated with finite Frobenius groups with complements of even order, and let $i$ be an involution of $G$. If, for some elements $a,b\in G$ with the condition $|a|\cdot|b|>4$, all subgroups $\langle a,b^g\rangle$, where $g\in G$, are finite, then $G=A\leftthreetimes C_G(i)$ is a Frobenius group with Abelian kernel $A$ and complement $C_G(i)$ whose elementary Abelian subgroups are all cyclic.
Keywords: groups saturated with groups
Mots-clés : Frobenius group. 
@article{AL_2021_60_6_a3,
     author = {B. E. Durakov},
     title = {Groups saturated with finite {Frobenius} groups with complements of even order},
     journal = {Algebra i logika},
     pages = {569--574},
     publisher = {mathdoc},
     volume = {60},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_6_a3/}
}
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B. E. Durakov. Groups saturated with finite Frobenius groups with complements of even order. Algebra i logika, Tome 60 (2021) no. 6, pp. 569-574. http://geodesic.mathdoc.fr/item/AL_2021_60_6_a3/