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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
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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

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4. Jacobson, N., Structure of rings, Amer. Math. Soc. Colloq. Pub., vol. 37.Google Scholar