Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-21T19:58:59.476Z Has data issue: false hasContentIssue false

P-groups with non-abelian automorphism groups and all automorphisms central

Published online by Cambridge University Press:  17 April 2009

J. J. Malone
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts, 01609, U. S. A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For each odd prime p this paper gives an example of a non-abelian p-group with a non-abelian automorphism group in which each automorphism is central.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Curran, M.J., “A non-abelian automorphism group with all automorphisms central”, Bull. Austral. Math. Soc. 26 (1982), 393397.CrossRefGoogle Scholar
[2]Faudree, R., “Groups in which each element commutes with its endomorphic images”. Proc. Amer. Math. Soc. 27 (1971), 236240.CrossRefGoogle Scholar
[3]Jonah, P. and Konvisser, M., “Some non-abelian p-groups with abelian automorphism groups”, Arch. Math. (Basel) 26 (1975), 131133.CrossRefGoogle Scholar
[4]Malone, J.J., “More on groups in which each element commutes with its endomorphic images”. Proc. Amer. Math. Soc. 65 (1977), 209214.CrossRefGoogle Scholar
[5]Malone, J.J., “A non-abelian 2-group whose endomorphisms generate a ring, and other examples of E-groups”, Proc. Edinburgh Math. Soc. 23 (1980), 5759.CrossRefGoogle Scholar