Solvable intransitive permutation groups with constant movement

Rezaei, Mehdi; Alaeiyan, Mehdi; Foruzanfar, Zeinab

doi:10.22103/jmmr.2024.23569.1666

Solvable intransitive permutation groups with constant movement

Document Type : Research Paper

Authors

Mehdi Rezaei ¹

Mehdi Alaeiyan ²

Zeinab Foruzanfar ¹

¹ Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran

² Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran

10.22103/jmmr.2024.23569.1666

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

Subjects

Algebra

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