Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2025-01-04T07:50:12.339Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Prime-Power Groups

Published online by Cambridge University Press:  20 November 2018

Ruth Rebekka Struik
Ruth Rebekka Struik*
Affiliation:
University of British Columbia
Rights & Permissions [Opens in a new window]

Extract

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 paper an unsuccessful attempt to classify prime - power groups is described. The attempt consisted in combining some ideas of P.Hall and O. N. Golovin.

Golovin [2] defined nilpotent products of groups and showed that every nilpotent group is a factor group of a nilpotent product of cyclic groups.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 3 , Issue 1 , 01 January 1960 , pp. 27 - 30
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Burnside, W., Theory of Groups of Finite Order, 2nd. ed., (New York, 1955).Google Scholar
2. Golovin, O. N., Nilpotent products of groups, Mat. Sbornik 27(69) (1950), 427-454. Amer. Math. Soc. Translations (2) 2 (1956), 89-115.Google Scholar
3. Golovin, O. N., The metabelian products of groups, Mat.Sbornik 28(70) (1951), 431-444. Amer. Math. Soc, Translations (2) 2 (1956), 117-132.Google Scholar
4. Golovin, O. N., On the isomorphism of nilpotent decompositions of groups, Mat.Sbornik 28(70) (1951), 445-452. Amer, Math. Soc. Translations (2) 2 (1956),133-140.Google Scholar
5. Hall, P., The classification of prime-power groups, J. reine angew. Math. 182 (1940), 130-140.Google Scholar
6. Magnus, W., ?ber Beziehungen zwischen h?heren Kommutatoren, J. reine angew. Math. 177 (1937), 105-115.Google Scholar
7. Moran, S., Associative operations on groups II, Proc. London Math. Soc. (3) 8 (1958), 548-568.Google Scholar
8. Struik, R. R., Notes on a paper by Sanov, Proc. Amer. Math, Soc, 8 (1957), 638-641.Google Scholar
9. Struik, R. R., On nilpotent products of cyclic groups, to appear in Can. J. Math.Google Scholar