Abelian Group Theory pp 671-684 | Cite as
Singly Generated Socles and Radicals
Chapter
Abstract
Socles, radicals, and socle-radicals have long been an object of study in abelian groups (and in modules). In this paper we consider the “building blocks” for socles and radicals — those determined by a single group. These are called singly generated. This paper addresses the question of when these singly generated socles (radicals) are also radicals (socles). This problem is equivalent to the question of when certain classes (determined by a single group) are closed under extensions.
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© Springer-Verlag Berlin Heidelberg 1983