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On linear p-groups

Published online by Cambridge University Press:  09 April 2009

W. J. Wong
W. J. Wong
Affiliation:
University of Otago
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A quasi-permutation group of degree n was defined in [3] to be a finite group with a faithful representation of degree n whose character has only non-negative rational integral values. If G is such a group, then the following simple properties of permutation groups of degree n were proved to hold also for G:

(i) the order of G is a divisor of the order of the symmetric group Sn of degree n; and (ii) if G is a p-group and n < p2, then G has exponent at most p and derived length at most 1 (i.e. G is elementary Abelian).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 2 , May 1964 , pp. 174 - 178
Copyright
Copyright © Australian Mathematical Society 1964

References

[1]Kaloujnine, L., La structure des p-groupes de Sylow des groupes symétriques finis, Ann. sci. École norm. sup. (3) 65, 239–276 (1948).CrossRefGoogle Scholar
[2]Miller, G. A., Blichfeldt, H. F. and Dickson, L. E., Theory and Applications of Finite Groups (New York, 1938).Google Scholar
[3]Wong, W. J., Linear groups analogous to permutation groups, Jour. Australian Math. Soc. 3, 180–184 (1963).CrossRefGoogle Scholar