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A note on theorem of Sah

Published online by Cambridge University Press:  17 April 2009

R. McGough
R. McGough
Affiliation:
University of Tasmania, Hobart, Tasmania.
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Abstract

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In this note we show that if H is any subgroup of the finite group G and if D is a normal subgroup of H such that H/D is soluble and the order of H/D is relatively prime to the index of B in G then the existence of a normal subgroup N of G such that NH = G and N ∩ H is contained in D is equivalent to the condition that every irreducible character of H/D can be extended to one of G. This is a generalization of a result due to Sah for the case when D is the identity subgroup.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 2 , October 1970 , pp. 269 - 271
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Hall, Marshall Jr, The theory of groupa (MacMillan, New York, 1959).Google Scholar
[2]Sah, Chih-Han, “Existence of normal complements and extension of characters in finite groups”, Illinois J. Math. 6 (1962), 282–291.CrossRefGoogle Scholar
[3]Suzuki, Michio, “On the existence of a normal Hall subgroup”, J. Math. Soc. Japan 15 (1963), 387–391.Google Scholar