Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T11:13:27.971Z Has data issue: false hasContentIssue false
  • English
  • Français

On Associative Compositions in Finite Nilpotent Groups

Published online by Cambridge University Press:  22 January 2016

Nagayosi Iwahori and
Akira Hattori
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.

Let

(1)

be a word in two variables X, Y, i.e. an element in the free group F2 on two generators X, Y. Let us say that f defines an associative composition for a group G if for arbitrary elements a, b, c in G we have

(2)

where a ° b is defined by

(3)

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 7 , June 1954, pp. 145 - 148
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1954

References

1 Iwasawa, K., Einige Satze uber freie Gruppen, Proc. Imp. Acad. Japan, 19 (1943), pp. 272–274 Google Scholar.

2 Note that is a central subgroup of Then for every a, b in G, c, d in we have (cf. H. Zassenhaus, Lehrbuch der Gruppentheorie, S. 57). The assertion is then completed by induction on i.