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A Note on Subnormal Subgroups of Division Algebras

Published online by Cambridge University Press:  20 November 2018

Gary R. Greenfield
Gary R. Greenfield*
Affiliation:
Wayne State University, Detroit, Michigan
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Let D be a division algebra and let D* denote the multiplicative group of nonzero elements of D. In [3] Herstein and Scott asked whether any subnormal subgroup of D* must be normal in D*. Our purpose here is to show that division algebras over certain p-local fields do not satisfy such a “subnormal property”.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 1 , 01 February 1978 , pp. 161 - 163
Copyright
Copyright © Canadian Mathematical Society 1978

References

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2. Herstein, I. N., Conjugates in division rings, Proc. Amer. Math. Soc. 2 (1956), 1021–1022.Google Scholar
3. Herstein, I. N. and Scott, W. R., Subnormal subgroups of division rings, Can. J. Math. 15 (1963), 80–83.Google Scholar
4. Riehm, C., The norm 1 group of p-adic division algebra, Amer. J. Math. 92 (1970), 499–523.Google Scholar
5. Steenrod, N. E., The topology of fibre bundles (Princeton University Press, Princeton, 1951).Google Scholar