Groups whose same-order types are arithmetic progressions

Mihai-Silviu Lazorec; Marius Tarnauceanu

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arXiv · 2012.10653

Groups whose same-order types are arithmetic progressions

Mihai-Silviu Lazorec·Marius Tarnauceanu

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Abstract

The same-order type $\tau_e(G)$ 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.

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Mihai-Silviu Lazorec, Marius Tarnauceanu. 2020-12-19. Groups whose same-order types are arithmetic progressions. https://arxiv.org/abs/2012.10653

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