Minimal odd order automorphism groups

Abstract

Abstract. We show that 3 7 is the smallest order of a non-trivial odd order group which occurs as the full automorphism group of a finite group.

Inversion is Possible in Groups with no Periodic Automorphisms

“…If G is finitely presented, then so is G * . Thus, if p and q are odd and G is a torsionfree group in which some element is conjugate to its inverse, for example, the fundamental group of the Klein bottle, then G * will be a group of the type asked for by Hegarty and MacHale [6]. This raises the question of whether one might adapt the construction of [12] to ensure that G * is torsion free if G is.…”

“…If a finite group G has an automorphism sending an element of order greater than 2 to its inverse, then G has an automorphism of order 2. Hegarty and MacHale [6] enquired about the corresponding statement for infinite groups. Theorem 1.1.…”