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Engel Congruences in Groups of Prime-Power Exponent

Published online by Cambridge University Press:  20 November 2018

George Glauberman ,
Eugene F. Krause  and
Ruth Rebekka Struik
George Glauberman
Affiliation:
University of Wisconsin, University of Michigan and University of Colorado, Pueblo, Colorado
Eugene F. Krause
Affiliation:
University of Wisconsin, University of Michigan and University of Colorado, Pueblo, Colorado
Ruth Rebekka Struik
Affiliation:
University of Wisconsin, University of Michigan and University of Colorado, Pueblo, Colorado
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In this paper a simplified proof of a theorem of Sanov (4) is given. No mention is required of Lie elements or of the Baker-Hausdorff formula, both of which played central roles in Sanov's proof.

Let G be a group. Define, for all x, y ∈ G,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 579 - 588
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Bruck, R. H., On the restricted Burnside problem, Arch. Math., 13 (1962), 179–186.Google Scholar
2. Hall, Marshall Jr., The theory of groups (New York, 1959).Google Scholar
3. Krause, Eugene F., Ph.D. Thesis, University of Wisconsin, 1963.Google Scholar
4. Sanov, I. N., On a certain system of relations in periodic groups with period a power of a prime, number. Izv. Akad. Nauk SSSR, Ser. Mat., 15 (1951), 477–502.Google Scholar