Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-10T00:25:14.090Z Has data issue: false hasContentIssue false
  • English
  • Français

The power structure of finite p-groups

Published online by Cambridge University Press:  17 April 2009

Mingyao Xu
Mingyao Xu
Affiliation:
Department of Mathematics, Peking University, Beijing, People's Republic of China and Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6009, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this survey article we give an exposition of some work on the power structure of p-groups; especially work of the author's. The titles of the three sections are: Section 1. p-groups which have regular power structure; Section 2. Some weaker power structure properties; Section 3. p-central series of p-groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 1 , August 1987 , pp. 1 - 10
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Arganbright, D.E., “The power-commutator structure on finite p-groups”, Pacific J. Math. 29 (1969), 11–17.CrossRefGoogle Scholar
[2]Brisley, W. and Macdonald, I.D., “Two classes of metabelian p-groups”, Math. Z. 112 (1969), 5–12.CrossRefGoogle Scholar
[3]Hall, P., “A contribution to the theory of groups of prime-power order”, Proc. London Math. Soc. 36 (1934), 29–95.CrossRefGoogle Scholar
[4]Hobby, C., “A characteristic subgroup of a p-group”, Pacific J. Math. 10 (1960), 853–858.CrossRefGoogle Scholar
[5]Huppert, B., Endliche Gruppen I, (Springer-Verlag, 1967).CrossRefGoogle Scholar
[6]King, B.W., “Presentations of metacyclic groups”, Bull. Austral. Math. Soc. 8 (1973), 101–131.CrossRefGoogle Scholar
[7]Mann, A., “The power structure of p-groups I”, J. Algebra 42 (1976), 121–135.CrossRefGoogle Scholar
[8]Tuan, H.F., “Works on finite group theory by some Chinese mathematicians”, Proc. of Symposia in Pure Math. 37 (1980), 187–194.CrossRefGoogle Scholar
[9]Wang, R.J., “On the power structure of finite p-groups” (in Chinese) Acta Math. Sinica. 29 (1986), 847–852.Google Scholar
[10]Xu, M.Y., On finite regular p-groups (in Chinese), (Graduation Thesis in Peking University, 1964).Google Scholar
[11]Xu, M.Y., “Semi-p-abelian p-groups and their power structure” (in Chinese), Acta Math. Sinica 23 (1980), 78–87.Google Scholar
[12]Xu, M.Y., “A class of semi-p-abelian p-groups” (in Chinese), Kexue Tongbao 26 (1981), 453–456. English translation in Kexue Tongbao (English Ed.) 27 (1982), 142–146.Google Scholar
[13]Xu, M.Y., “A theorem on metabelian p-groups and some consequences”, Chinese Ann. Math. Ser. B. (English Ed.) 5 (1984), 1–6.Google Scholar
[14]Xu, M.Y., “On the power structure of finite 3-groups” (in Chinese) Acta Math. Sinica 27 (1984), 721–729.Google Scholar
[15]Xu, M.Y. and Yang, Y.C., “Semi-p-commutativity and regularity of finite p-groups” (in Chinese), Acta Math. Sinica 19 (1976), 281–285.Google Scholar