On the structure of some non-periodic groups whose subgroups of infinite special rank are transitively normal

Keywords: special rank, transitively normal subgroup
Published online: 2021-11-02

Abstract


A group $G$ has a finite special rank $r$ if every finitely generated subgroup of $G$ is generated by at most $r$ elements and there is a finitely generated subgroup of $G$ which has exactly $r$ generators. If there is not such $r$, then we say that $G$ has infinite special rank. In this paper, we study generalized radical non-abelian groups of infinite special rank whose subgroups of infinite special rank are transitively normal.

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How to Cite
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VelychkoT. On the Structure of Some Non-Periodic Groups Whose Subgroups of Infinite Special Rank Are Transitively Normal. Carpathian Math. Publ. 2021, 13, 515-521.