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On a Theorem Of Baer and Higman

Published online by Cambridge University Press:  20 November 2018

Seân Tobin
Seân Tobin*
Affiliation:
University College, Galway, Ireland
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1.1 Baer has shown (1) that if the fact that the exponent of a group is m (that is, m is the least common multiple of the periods of the elements) implies a limitation on the class of the group, then m must be a prime. Graham Higman has extended this result by proving (3) that for any given integer M there are at most a finite number of prime powers q other than primes, such that the fact that a group has exponent q implies a limitation on the class of the Mth derived subgroup.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 263 - 270
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Baer, R., The higher commutator subgroups of a group., Bull. Amer. Math. Soc, 50 (1944), 143–160.Google Scholar
2. Hall, P., A contribution to the theory of groups of prime power order, Proc. Lond. Math. Soc., 36 (1933), 29–95.Google Scholar
3. Higman, G., Note on a theorem of R. Baer, Proc. Camb. Phil. Soc, 45 (1949), 321–327.Google Scholar
4. Meier-Wunderli, H., Über endliche p-Gruppen deren Elemente der Gleichung xp = 1 geniigen, Comment. Math. Helv., 24 (1950), 18–45.Google Scholar
5. Sanov, I. N., Solution of Burnside's Problem for exponent 4, Leningrad State Univ. Annals, Math. Ser., 10 (1940), 166–170 Google Scholar