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On cyclic subgroups of finite groups
| Content Provider | Scilit |
|---|---|
| Author | Dempwolff, U. Wong, S. K. |
| Copyright Year | 1982 |
| Description | In [3] Laffey has shown that if Z is a cyclic subgroup of a finite subgroup G, then either a nontrivial subgroup of Z is normal in the Fitting subgroup F(G) or there exists a g in G such that $Z^{g}$∩Z = 1. In this note we offer a simple proof of the following generalisation of that result:Theorem. Let G be a finite group and X and Y cyclic subgroups of G. Then there exists a g in G such that $X^{g}$∩Y⊴F(G). |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/DB19988BD9CD986D3F122F74CC5004F2/S0013091500004065a.pdf/div-class-title-on-cyclic-subgroups-of-finite-groups-div.pdf |
| Ending Page | 20 |
| Page Count | 2 |
| Starting Page | 19 |
| ISSN | 00130915 |
| e-ISSN | 14643839 |
| DOI | 10.1017/s0013091500004065 |
| Journal | Proceedings of the Edinburgh Mathematical Society |
| Issue Number | 1 |
| Volume Number | 25 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1982-02-01 |
| Access Restriction | Open |
| Subject Keyword | Proceedings of the Edinburgh Mathematical Society |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
