Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-16T15:40:01.354Z Has data issue: false hasContentIssue false
  • English
  • Français

Subnormal Subgroups of Division Rings

Published online by Cambridge University Press:  20 November 2018

I. N. Herstein  and
W. R. Scott
I. N. Herstein
Affiliation:
Cornell University, The University of Kansas
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 K be a division ring. A subgroup H of the multiplicative group K′ of K is subnormal if there is a finite sequence (H = A0, A1, . . . , An = K′) of subgroups of K′ such that each Ai is a normal subgroup of Ai+1. It is known (2, 3) that if H is a subdivision ring of K such that H′ is subnormal in K′, then either H = K or H is in the centre Z(K) of K.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 80 - 83
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Huzurbazar, M., The multiplicative group of a division ring, Dok. Akad. Nauk, 131 (1960), 1268–1271. (Translation of Doklady, 1, No. 2, 433.)Google Scholar
2. Schenkman, Eugene, Some remarks on the multiplicative group of a sfield, Proc. Amer. Math. Soc, 9 (1958), 231–235.Google Scholar
3. Schenkman, Eugene and Scott, W. R., A generalization of the Cartan-Brauer-Hua theorem, Proc. Amer. Math. Soc, 11 (1960), 396–398.Google Scholar
4. Jacobson, N., Structure of rings, Amer. Math. Soc. Colloq. Pub., vol. 37.Google Scholar