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Totally disconnected groups and proofs of conjectures of Hofmann and Mukherjea

Published online by Cambridge University Press:  17 April 2009

George Willis
George Willis
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, NSW 2308, Australia, e-mail: [email protected]
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Abstract

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Some structure theorems for totally disconnected groups are described. These theorems produce a certain positive integer valued function, called the scale function, on each totally disconnected group. The scale function has properties connected to the structure of the group and can be used to prove some conjectures of Hofmann and Mukherjea.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 3 , June 1995 , pp. 489 - 494
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Bourbaki, N., General topology Part 1 (Herman, Paris, 1966).Google Scholar
[2]Bourbaki, N., Lie Groups and Lie Algebras (Springer-Verlag, Berlin, Heidelberg, New York, 1980).Google Scholar
[3]Hewitt, E. and Ross, K.A., Abstract Harmonic Analysis (Springer-Verlag, Berlin, Gottingen, Heidelberg, 1963 and 1970).Google Scholar
[4]Hofmann, K.H., ‘Characteristic subgroups in locally compact totally disconnected groups and their applications to a problem on random walks on locally compact groups’, Technische Hochschule Darmstadt, Fachbereich Mathematik Preprint Series 606 (1981), 1–12.Google Scholar
[5]Hofmann, K.H. and Mukherjea, A., ‘Concentration functions and a class of non-compact groups’, Math. Ann. 256 (1981), 535–548.CrossRefGoogle Scholar
[6]Gleason, A.M., ‘Groups without small subgroups’, Ann. of Math. 56 (1952), 193–212.CrossRefGoogle Scholar
[7]Grosser, S. and Moskowitz, M., ‘Compactness conditions in topological groups’, J. Reine Angew. Math. 246 (1971), 1–40.Google Scholar
[8]Kaplansky, I., Lie Algebras and Locally Compact Groups (Univ. Chicago Press, Chicago and London, 1974).Google Scholar
[9]Montgomery, D. and Zippin, L., Topological Transformation Groups (Interscience Publishers, New York, 1955).Google Scholar
[10]Pontryagin, L., Topological groups, (English translation of 1939 Russian edition) (Princeton U.P., Princeton, 1946).Google Scholar
[11]Rosenblatt, J.M. and Willis, G.A., ‘Concentration functions in locally compact groups’ (to appear).Google Scholar
[12]van Dantzig, D., ‘Zur topologischen Algebra III. Brouwersche und Cantorsche Gruppen’, Compositio Math. 3 (1936), 408–426.Google Scholar
[13]Willis, G.A., ‘The structure of totally disconnected, locally compact groups’, Math. Ann. (to appear).Google Scholar