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2-groups of almost maximal class

Published online by Cambridge University Press:  09 April 2009

Rodney James
Rodney James
Affiliation:
The University of New South WalesSydney, Australia
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Let G be a group of order 2n and x, y ∈ G. We define the Commutator [x, y] as x−1y−1xy. Similarly, if X, Y are subsets of G, then [X, Y] denotes the sub-group genrated by all commutators of the form [x, y] where x ∈ X, y ∈ Y. Using this, we may define the lower central series of G inductively by The following results are well known.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 3 , May 1975 , pp. 343 - 357
Copyright
Copyright © Australian Mathematical Society 1975

References

Blackburn, N. (1958), ‘On a special class of p-groups’, Acta Math. 100, 45–92.CrossRefGoogle Scholar
Blackburn, N. (1957), ‘On prime-power groups in which the derived group has two generators’, Proc. Camb. Phil. Soc. 53, 19–27.CrossRefGoogle Scholar
Hall, M. and Senior, J. K. (1964), The Groups of Order an; (n ≦ 6), (The Macmillan Company, New York, 1964).Google Scholar
Hall, P. (1933), ‘A Contribution to the theory of groups of prime-power order’, Proc. Lond. Matk. Soc. (2) 36, 29–95.Google Scholar
James, R. and Cannon, J. (1969), ‘Computation of isomorphism classes of p-groups’, Maths. of Computation 23, 135–140.Google Scholar