Criterions of supersolubility of some finite factorizable groups
Algebra and discrete mathematics, no. 3 (2005), pp. 46-55
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Let $A$, $B$ be subgroups of a group $G$ and $\emptyset\ne X\subseteq G$. A subgroup $A$ is said to be $X$-permutable with $B$ if for some $x\in X$ we have $AB^x=B^xA$ [1]. We obtain some new criterions for supersolubility of a finite group $G=AB$, where $A$ and $B$ are supersoluble groups. In particular, we prove that a finite group $G=AB$ is supersoluble provided $A$, $B$ are supersolube subgroups of $G$ such that every primary cyclic subgroup of $A$ $X$-permutes with every Sylow subgroup of $B$ and if in return every primary cyclic subgroup of $B$ $X$-permutes with every Sylow subgroup of $A$ where $X=F(G)$ is the Fitting subgroup of $G$.
Keywords:
finite group, supersoluble group, permutable subgroups, product of subgroups.
@article{ADM_2005_3_a3,
author = {Helena V. Legchekova},
title = {Criterions of supersolubility of some finite factorizable groups},
journal = {Algebra and discrete mathematics},
pages = {46--55},
publisher = {mathdoc},
number = {3},
year = {2005},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ADM_2005_3_a3/}
}
Helena V. Legchekova. Criterions of supersolubility of some finite factorizable groups. Algebra and discrete mathematics, no. 3 (2005), pp. 46-55. http://geodesic.mathdoc.fr/item/ADM_2005_3_a3/