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Yutao Jin, Finite 2-groups whose the same-order type is arithmetic progressions, Eur. J. Math. Appl. 4 (2024), Article ID 21.

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Volume 4 (2024), Article ID 21

https://doi.org/10.28919/ejma.2024.4.21

Published: 24/09/2024

Abstract:

The same-order type $\tau_e(G)$ of a finite group $G$ is a set formed from the sizes of the equivalence classes containing elements of the same order in $G$. Lazorec and Tarnauceanu [2] posed an open question about the groups whose same-order type consists of an arithmetic progression with $3$ elements in $2$-group. In this paper, we prove that the same-order type of a metacyclic group can not be an arithmetic progression. We also discussed that the arithmetic progression of an abelian group and the extension of an abelian group.

How to Cite:

Yutao Jin, Finite 2-groups whose the same-order type is arithmetic progressions, Eur. J. Math. Appl. 4 (2024), Article ID 21. https://doi.org/10.28919/ejma.2024.4.21