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Mathematics > Group Theory

arXiv:1405.6518 (math)
This paper has been withdrawn by Mohammad Shahryari
[Submitted on 26 May 2014 (v1), last revised 13 Jul 2014 (this version, v2)]

Title:A note on groups with self-normalizing cyclic subgroups

Authors:M. Shahryari
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Abstract:In this article, we prove that if all non-trivial cyclic subgroups of a group $G$ are self normalizing and $G$ satisfies the implication $$ \ o(x)\neq o(y)\Rightarrow o(xy)\neq o(x), o(y), $$ for all non-trivial elements $x$ and $y$, then $G$ is a $p$-group or simple.
Comments: This article is withdrawn, because the main result can be proved in more general frame of TC-groups
Subjects: Group Theory (math.GR)
MSC classes: Primary 20N07, Secondary 20F06
Cite as: arXiv:1405.6518 [math.GR]
  (or arXiv:1405.6518v2 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.1405.6518

Submission history

From: Mohammad Shahryari [view email]
[v1] Mon, 26 May 2014 09:39:16 UTC (4 KB)
[v2] Sun, 13 Jul 2014 08:17:54 UTC (1 KB) (withdrawn)
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