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Cyclic permutable subgroups of finite groups
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Cossey, John, 1941- and Stonehewer, Stewart E. (Stewart Edward), 1935-. (2001) Cyclic permutable subgroups of finite groups. Journal of the Australian Mathematical Society, Vol.71 (No.2). pp. 169-176. ISSN 1446-7887
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Official URL: http://dx.doi.org/10.1017/S1446788700002810
Abstract
The authors describe the structure of the normal closure of a cyclic permutable subgroup of odd order in a finite group.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Finite groups, Subnormal operators, Group theory, Products of subgroups, Cyclic permutations |
| Journal or Publication Title: | Journal of the Australian Mathematical Society |
| Publisher: | Cambridge University Press |
| ISSN: | 1446-7887 |
| Date: | October 2001 |
| Volume: | Vol.71 |
| Number: | No.2 |
| Page Range: | pp. 169-176 |
| Identification Number: | 10.1017/S1446788700002810 |
| Status: | Peer Reviewed |
| Access rights to Published version: | Open Access |
| References: | [1] Berger, T. E. and Gross, F., ‘A universal example of a core-free permutable subgroup’, Rocky Mountain J. Math. 12 (1982), 345–365. [2] Bradway, R. H., Gross, F. and Scott, W. R., ‘The nilpotence class of core-free permutable subgroups’, Rocky Mountain J. Math. 1 (1971), 375–382. [3] Cooper, C. D. H., ‘Power automorphism of a group’, Math. Z. 107 (1968), 335–356. [4] Huppert, B., ‘Über das Produkt von paarweise vertauschbaren zyklischen Gruppen’, Math. Z. 58 (1953), 243–264. [5] Itô, N. and Szép, J., ‘Über die Quasinormalteiler von endlichen Gruppen’, Acta Sci. Math. (Szeged) 23 (1962), 168–170. [6] Maier, R. and Schmid, P., ‘The embedding of permutable subgroups in finite groups’, Math. Z. 131 (1973), 269–272. [7] Ore, O., ‘On the application of structure theory to groups’, Bull. Amer. Math. Soc. 44 (1938), 801–806. [8] Robinson, D. J. S., A course in the theory of groups, Graduate Texts in Math. 80, 2nd edition (Springer, New York, 1996). [9] Schmidt, R., Subgroup lattices of groups (Walter de Gruyter, Berlin, 1994). [10] Stonehewer, S. E., ‘Permutable subgroups of infinite groups’, Math. Z. 125 (1972), 1–16. [11] Stonehewer, S. E., ‘Permutable subgroups of some finite p-groups’, J. Austral. Math. Soc. 16 (1973), 90–97. [12] Stonehewer, S. E., ‘Permutable subgroups of some finite permutation groups’, Proc. London Math. Soc. (3) 28 (1974), 222–236. [13] Thompson, J. G., ‘An example of core-free permutable subgroups of p-groups’, Math. Z. 96 (1967), 226–227. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/814 |
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