Groups whose same-order types are arithmetic progressions

Abstract

The same-order type τ_e(G) of a finite group G is a set formed of the sizes of the equivalence classes containing the same order elements of G. In this paper, we study an arithmetical property of this set. More exactly, we outline some results on the classification and existence of finite groups whose same-order types are arithmetic progressions formed of 3 or 4 elements, the latter being the maximum size of such a sequence.

Mathematics Subject Classification (2020):

• Primary: 20D60
• Secondary: 20D15

Key words:

• Group element orders
• same-order type of a group
• arithmetic progression