Real genus of minimal nonnilpotent groups (Q706003)

Given a finite group \(G\), the real genus of \(G\) is defined as the minimum algebraic genus of compact bordered Klein surfaces on which \(G\) acts as a group of automorphisms. A group \(G\) is minimal non-nilpotent if it is not nilpotent, but each of its maximal subgroups is nilpotent. The authors obtain a lower bound for the real genus of a minimal non-nilpotent group. The arguments involve NEC groups, their presentations and the fact that a minimal non-nilpotent group has order \(p^{a}q^{b}\), where \(p\) and \(q\) are different primes.