2018
Том 70
№ 9

# On primarily factorable groups

Gогсhаkоv Y. M.

Abstract

In the present paper the author solves the question of the structure of groups with complemented $p$-subgroups (a subgroup $\mathfrak{U}$ of a group $\mathfrak{G}$ is said to be complemented in $\mathfrak{G}$ if there exists in $\mathfrak{G}$ such a subgroup $\mathfrak{B}$ that $\mathfrak{UB} = \mathfrak{G}$ and $\mathfrak{U} \bigcap \mathfrak{B} = 1$ which was suggested to the author by S. N. Chernikov. If the group is periodical, the necessary and sufficient conditions are given for the p-subgroups of the group to be complemented in it. It is also shown that in general not every subgroup of a periodical group is complemented if all its $p$-subgroups are complemented.

Citation Example: Gогсhаkоv Y. M. On primarily factorable groups // Ukr. Mat. Zh. - 1962. - 14, № 1. - pp. 3-9.

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