关于初等阿贝尔群和超特殊$p$-群的幂图

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2020-03-25 DOI:10.22108/IJGT.2020.120552.1588

M. Pourhasan, H. Doostie

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引用次数: 0

摘要

‎对于给定的奇数素数$p$‎, ‎我们‎ ‎三的幂图研究‎ ‎有限群的类‎: ‎初等‎ ‎指数$p的阿贝尔群$‎, ‎以及‎ ‎特殊指数组$p$或‎ ‎$p^2$‎. ‎我们展示了这些功率图‎ ‎每$p是欧拉的吗$‎. ‎作为‎ ‎推论‎, ‎我们描述了两类‎ ‎具有同构的非同构群‎ ‎功率图‎. ‎此外‎, ‎我们证明‎ ‎的幂图的团图‎ ‎两个考虑的类是完整的‎.

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On the power graphs of elementary abelian and extra special $p$-groups

‎For a given odd prime $p$‎, ‎we‎ ‎investigate the power graphs of three‎ ‎classes of finite groups‎: ‎the elementary‎ ‎abelian groups of exponent $p$‎, ‎and the‎ ‎extra special groups of exponents $p$ or‎ ‎$p^2$‎. ‎We show that these power graphs‎ ‎are Eulerian for every $p$‎. ‎As a‎ ‎corollary‎, ‎we describe two classes of‎ ‎non-isomorphic groups with isomorphic‎ ‎power graphs‎. ‎In addition‎, ‎we prove that‎ ‎the clique graphs of the power graphs of‎ ‎two considered classes are complete‎.

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来源期刊

International Journal of Group Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

30 weeks

期刊介绍： International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.