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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

IMPACT FACTOR 2018: 0.470
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CiteScore 2018: 0.53

SCImago Journal Rank (SJR) 2018: 0.566
Source Normalized Impact per Paper (SNIP) 2018: 1.047

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Volume 18, Issue 6


The absolute center of finite groups

Hangyang Meng / Xiuyun Guo
Published Online: 2015-04-28 | DOI: https://doi.org/10.1515/jgth-2015-0015


In this paper we first investigate the relationship between the absolute center L(G) and the Frattini subgroup Φ(G) for a finite group G, and then we describe the structure of finite groups G satisfying L(G) ≤ Φ(G). For example, we prove that a finite group G is an ℱ-group if and only if G/L(G) is an ℱ-group, where ℱ is a saturated formation containing Z2. Next we determine all finite groups X such that X/L(X) is isomorphic to Zpω × Zp, where ω is a positive integer and Zpω is a cyclic group of order pω.

About the article

Received: 2014-11-20

Revised: 2015-02-18

Published Online: 2015-04-28

Published in Print: 2015-11-01

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11371237

Funding Source: “The First-Class Discipline of Universities in Shanghai”

Citation Information: Journal of Group Theory, Volume 18, Issue 6, Pages 887–904, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgth-2015-0015.

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