Solvable intransitive permutation groups with constant movement

Abstract

In this paper, all solvable intransitive permutation groups with constant movement are classified and we show that they are one of the following groups: a cyclic $p$-group, an elementary abelian $p$-group, a Frobenius group of order 12 or a Frobenius group of order $pq$, where $p$ and $q$ are primes such that $p=q(q-1)+1.$

Keywords

• permutation group
• orbit
• constant movement
• frobenius group