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On normaliser preserving lattice isomorphisms between nilpotent groups

Published online by Cambridge University Press:  09 April 2009

D. W. Barnes  and
G. E. Wall
D. W. Barnes
Affiliation:
Mathematics Department, University of Sydney.
G. E. Wall
Affiliation:
Mathematics Department, University of Sydney.
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Let (G) denote the lattice of all subgroups of a group G. By an -isomorphism (lattice isomorphism) of G onto a group H, we mean an isomorphism of (G) onto (H). By an -isomorphism (normaliser preserving -isomorphism) of G onto H, we mean an -isomorphism ø such that (Aø) = (A)ø for all A ∈ (G). In this paper, we study certain properties of groups which remain invariant under -isomorphisms.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 4 , November 1964 , pp. 454 - 469
Copyright
Copyright © Australian Mathematical Society 1964

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