Pentactions and action representability in the category of reduced groups with action

Abstract

A notion of pentaction of any object in the category ${\mathbf{rGr}}^{\bullet }$ of reduced groups with action is introduced. The operations are defined in the set $\mathsf{Pentact}(A)$ of pentactions of an object $A$ of ${\mathbf{rGr}}^{\bullet }$. It is proved that if an object $A$ is perfect with zero weak stabilizer in the sense defined in the paper, then $\mathsf{Pentact}(A)$ is an object of ${\mathbf{rGr}}^{\bullet }$, it has a derived action on $A$, the object $A$ is action representable and $\mathsf{Pentact}(A)$ represents all actions on $A$.

20 pages, research paper, LaTeX2e, xypic

References in corpus (1)

• Actions and semi-direct products in categories of groups with action

Cited by in corpus (1)

• Actions and semi-direct products in categories of groups with action