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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo


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ICV 2017: 161.82

Open Access
Online
ISSN
2391-5455
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Volume 11, Issue 10

Issues

Volume 13 (2015)

Groups where each element is conjugate to its certain power

Pál Hegedűs
Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0287-8

Abstract

This paper deals with a rationality condition for groups. Let n be a fixed positive integer. Suppose every element g of the finite solvable group is conjugate to its nth power g n. Let p be a prime divisor of the order of the group. We conclude that the multiplicative order of n modulo p is small, or p is small.

MSC: 20C20; 20D10; 20E45

Keywords: Finite solvable groups; Conjugacy criterion; Rationality

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About the article

Published Online: 2013-07-20

Published in Print: 2013-10-01


Citation Information: Open Mathematics, Volume 11, Issue 10, Pages 1742–1749, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0287-8.

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© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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