Marian Deaconescu: Three lemmas on commutators, 167-171

Abstract:

A group $G$, two subgroups $H, K$ of $G$ and a subgroup $A$ of $Aut(G)$ are considered. One looks for conditions on $G, H, K$, and $A$ ensuring that the set of all commutators $[g, a]$ with $g\in G$ and $a\in A$ is contained in the union $H\cup K$.

Key Words: commutators, automorphisms, orbits, fixed points.

2010 Mathematics Subject Classification: Primary 20D45. Secondary 20D60, 20F28.