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T2-Groups And a Characterization of the Finite Groups of Moebius Transformations

Published online by Cambridge University Press:  20 November 2018

P. J. Lorimer
P. J. Lorimer*
Affiliation:
University of Canterbury, Christchurch, New Zealand
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In recent years a number of algebraic characterizations of the groups of Moebius transformations over finite fields have been given in the literature; see (1, 3, 6). H. W. E. Schwerdtfeger has noticed (4) that the group G of Moebius transformations over the real, complex, and certain other fields has the property:

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 353 - 366
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Brauer, R., Suzuki, M., and Wall, G. E., A characterisation of the one-dimensional unimodular projective groups over finite fields, III. J. Math., 2 (1958), 718–45.Google Scholar
2. Burnside, W., Theory of groups of finite order (New York, 1955).Google Scholar
3. Gorenstein, Daniel and Walter, John H., On finite groups with dihedral Sylow 2-subgroups, III. J. Math., 6, (1962), 533–93.Google Scholar
4. E.|Schwerdtfeger, H. W., On a property of the Moebius group, Annali di Mat. (IV), 54 (1961), 23–32.Google Scholar
5. E.|Schwerdtfeger, H. W. Über eine spezielle Klasse Frobeniusscher Gruppen, Arch. d. Math., 13 (1962), 283–9.Google Scholar
6. Zassenhaus, H., Kennzeichnung endlicher linear er Gruppen als Per mutations gruppen, Abh. Math. Sem. Univ. Hamburg, 11 (1936), 17–40.Google Scholar