Marian Deaconescu, Gary Walls: Remarks on finite group actions, p. 225-231


The concept of control of fusion in a subgroup of a finite group is adapted to the more general situation of a finite group $A$ acting on a finite set $S$. This leads to a general version of a classical lemma of Burnside. When $A$ acts on a finite group $G$ via automorphisms we obtain a handful of general results related to $A$-invariant subgroups of $G$ and to the orbits of $A$ in $G$.

Key Words: actions, fixed points, orbits, control of fusion

2010 Mathematics Subject Classification: Primary 20D60
Secondary 20D25, 20C15, 20F12