Open AccessOn the structure of some non-periodic groups whose subgroups of infinite special rank are transitively normal
Author(s) -
T.V. Velychko
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.2.515-521
Subject(s) - mathematics , rank (graph theory) , abelian group , normal subgroup , combinatorics , finitely generated abelian group , group (periodic table) , pure mathematics , chemistry , organic chemistry
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.