Journal of Group Theory
Editor-in-Chief: Parker, Christopher W. / Wilson, John S.
Managing Editor: Howie, James / Khukhro, Evgenii I. / Kramer, Linus
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Anomalous behavior of the Hawaiian earring group
Citation Information: Journal of Group Theory. Volume 8, Issue 2, Pages 223–227, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/jgth.2005.8.2.223, July 2005
- 2 October, 2003
- 24 January, 2004
- Published Online:
Let H be the classical Hawaiian earring, and let G be its fundamental group, the Hawaiian earring group. We show that the structure of homomorphisms from the Hawaiian earring group to finite groups behaves in anomalous ways. In particular, there are uncountably many surjective homomorphisms of the Hawaiian earring group to any finite group which cannot be represented by continuous maps.