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A characterisation of the moebius and similarity groups

Published online by Cambridge University Press:  09 April 2009

P. J. Lorimer
P. J. Lorimer
Affiliation:
McGill University, Montreal, Quebec, Canada, University of Canterbury, Christchurch, New Zealand.
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Let PGL(2, F) denote the group of all Moebius transformations over a field F. In a recent paper [2], the author has given a characterisation of the groups PGL(2, F), F finite, char F ≠ 2. It is the purpose of this paper to give a similar characterisation of the group PGL (2, F), char F = 2, F finite or infinite.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 2 , May 1965 , pp. 237 - 240
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Feit, W., A Characterisation of the Simple Groups SL (2,2α), Amer. J. Math. 82 (1960), 281–300.Google Scholar
[2]Lorimer, P. J., T2-groups and a Characterisation of the Finite Groups of Moebius Transformations. To appear in the Canad. J. Math.Google Scholar
[3]Schwerdtfeger, H. W. E., Über eine spezielle Klasse Frobeniusscher Gruppen, Archiv der Math. 13 (1962), 283–289.Google Scholar
[4]Schwerdtfeger, H. W. E., On a property of the Moebius Group, Ann. di Mat. (4) 54 (1961), 23–32.Google Scholar
[5]Tits, J., Sur les groupes doublement transitifs continus, Comm. Math. Helvetici (26) 203–224.Google Scholar
[6]Zassenhaus, H., Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen, Abh. Math. Sem. Univ. Hamburg. 2 (1936), 17–40.Google Scholar