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A note on orthogonality and permutability of subnormal subgroups

Published online by Cambridge University Press:  24 October 2008

John C. Lennox
John C. Lennox
Affiliation:
University College, Cardiff
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Extract

Let H and K be groups with derived sub groups H´ and K´. Following (5) we say that H and K are orthogonal, and write H ⊥ K, if and only if the tensor product H/H´ ®K/K´ is trivial. If H and K are sub groups of a group we say that H and K permute if and only if HK = KH. We recall finally that the subgroup H of the group G is said to be subnormal in G, written H sn G, if and only if there exists a finite chain of subgroups

connecting H to G.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 351 - 355
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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