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Finite metacyclic groups all extensions of which split

Published online by Cambridge University Press:  14 November 2011

John S. Rose
John S. Rose
Affiliation:
Department of Pure Mathematics, University of Newcastle upon Tyne
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Synopsis

The groups of the title are characterized arithmetically.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 3-4 , 1978 , pp. 285 - 291
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Baer, R.Absolute retracts in group theory. Bull. Amer. Math. Soc. 52 (1946), 501–506.CrossRefGoogle Scholar
2Dark, R. S.A complete group of odd order. Math. Proc. Cambridge Philos. Soc. 11 (1975), 21–28.CrossRefGoogle Scholar
3Kaplansky, I.Infinite Abelian groups (Ann Arbor: Univ. Michigan Press, 1954).Google Scholar
4Miller, G. A.On the multiple holomorphs of a group. Math. Ann. 66 (1909), 133–144.CrossRefGoogle Scholar
5Rose, J. S.Splitting properties of group extensions. Proc. London Math. Soc. 22 (1971), 1–23.CrossRefGoogle Scholar
6Rose, J. S.Automorphism groups of groups with trivial centre. Proc. London Math. Soc. 31 (1975), 167–193.CrossRefGoogle Scholar
7Schenkman, E.The splitting of certain solvable groups. Proc. Amer. Math. Soc. 6 (1955), 286–290.CrossRefGoogle Scholar
8Szele, T.Über die direkten Teiler der endlichen Abelschen Gruppen. Comment. Math. Helv. 22 (1949), 117–124.CrossRefGoogle Scholar
9Horoševskiǐ, M. V.Complete groups of odd order. Algebra i Logika 13 (1973), 63–76, 121. English transl. Algebra and Logic 13 (1974), 34–40.Google Scholar