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The embedding of a cyclic permutable subgroup in a finite group. II
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Cossey, John, 1941- and Stonehewer, Stewart E. (Stewart Edward), 1935-. (2004) The embedding of a cyclic permutable subgroup in a finite group. II. Proceedings of the Edinburgh Mathematical Society (Series 2) , Vol.47 (No.2). pp. 101-109. ISSN 0013-0915
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Official URL: http://dx.doi.org/10.1017/S0013091502001062
Abstract
In two previous papers we established the structure of the normal closure of a cyclic permutable subgroup $A$ of a finite group, first when $A$ has odd order and second when $A$ has even order, but with an extra hypothesis that was unnecessary in the odd case. Here we describe the most general situation without any restrictions on $A$.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Group theory, Products of subgroups, Finite groups, Sylow subgroups, Automorphisms |
| Journal or Publication Title: | Proceedings of the Edinburgh Mathematical Society (Series 2) |
| Publisher: | Cambridge University Press |
| ISSN: | 0013-0915 |
| Date: | February 2004 |
| Volume: | Vol.47 |
| Number: | No.2 |
| Page Range: | pp. 101-109 |
| Identification Number: | 10.1017/S0013091502001062 |
| Status: | Peer Reviewed |
| Access rights to Published version: | Open Access |
| References: | 1. R. Baer, Situation der Untergruppen und Struktur der Gruppen, Sitz. Ber. Heidelberg Akad. 2 (1933), 12–17. 2. C. D. H. Cooper, Power automorphisms of a group, Math. Z. 107 (1968), 335–356. 3. J. Cossey and S. E. Stonehewer, Cyclic permutable subgroups of finite groups, J. Aust. Math. Soc. 71 (2001), 169–176. 4. J. Cossey and S. E. Stonehewer, The embedding of a cyclic permutable subgroup in a finite group, Illinois J. Math., in press. 5. R. Dedekind, Über Gruppen, deren sämtliche Teiler Normalteiler sind, Math. Annln 48 (1897), 548–561. 6. B. Huppert, Über das Produkt von paarweise vertauschbaren zyklischen Gruppen, Math. Z. 58 (1953), 243–264. 7. O. Ore, On the application of structure theory to groups, Bull. Am. Math. Soc. 44 (1938), 801–806. 8. D. J. S. Robinson, A course in the theory of groups, 2nd edn, Graduate Texts in Mathematics, vol. 80 (Springer, 1996). 9. R. Schmidt, Subgroup lattices of groups, Expositions in Mathematics, vol. 14 (de Gruyter, Berlin, 1994). |
| URI: | http://wrap.warwick.ac.uk/id/eprint/754 |
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