Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-14T07:24:42.541Z Has data issue: false hasContentIssue false
  • English
  • Français

A theorem on power-open LCA groups and its consequences

Published online by Cambridge University Press:  17 April 2009

M.A. Khan
M.A. Khan
Affiliation:
IC, 5/13, Nazimabad, Karachi, Pakistan.
Rights & Permissions [Opens in a new window]

Extract

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.

An LCA group G is called largely open if every large subgroup (that is, subgroup of finite index) of G is open. G is power-open if the continuous endomorphism, g → ng, g ∈ G, takes open sets of G onto open sets of G for every integer n > 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 26 , Issue 2 , October 1982 , pp. 239 - 247
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Fuchs, László, Infinite abelian groups, Volume I (Pure and Applied Mathematics, 36–I. Academic Press, New York and London, 1970).Google Scholar
[2]Hewitt, Edwin and Ross, Kenneth A., Abstract harmonic analysis I. Structure of topological groups, integration theory, group representations (Die Grundlehren der mathematischen Wissenschaften, 115. Springer-Verlag, Berlin, Heidelberg, New York, 1963).Google Scholar
[3]Hewitt, Edwin and Ross, Kenneth A., “Extensions of Haar measure and of harmonic analysis for locally compact abelian groups”, Math. Ann. 160 (1965), 171–194.Google Scholar
[4]Khan, M.A., “Chain conditions on subgroups of LCA groups”, Pacific J. Math. 86 (1980), 517–534.CrossRefGoogle Scholar
[5]Khan, M.A., “Power-rich and power-deficient LCA groups”, Canad. J. Math. 33 (1981), 664–670.CrossRefGoogle Scholar
[6]Khan, M.A., “When are proper subgroups of LCA groups contained in maximal ones?”, Proc. Amer. Math. Soc. 83 (1981), 131–137.CrossRefGoogle Scholar
[7]Peterson, H. Leroy, “Discontinuous characters and subgroups of finite index”, Pacific J. Math. 44 (1973), 683–691.Google Scholar
[8]Leroy Peterson, H., “Extensions of Haar measure to relatively large nonmeasurable subgroups”, Trans. Amer. Math. Soc. 228 (1977), 359–370.CrossRefGoogle Scholar
[9]Sharpe, Kevin J., “Relating group topologies by their continuous points”, Proc. Amer. Math. Soc. 57 (1976), 179–182.Google Scholar