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.

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