Monomiality and 2-isoclinism of groups

Abstract

A fair classification of groups of prime-power order can be given, when employing the equivalence relation brought out by Ph. Hall, called n-isoclinism (n≥0). In this paper n-isoclinism is studied from a character theoretic point of view in case n=0, 1 or 2. It is known that being an M-group is invariant under 1-isoclinism and that under 2-isoclinism this does not hold in general. However, under suitable oddness assumptions on the groups in question, the invariance under 2-isoclinism of being an M-group will be established in an important special case.