Vol. 80, No. 2, 1979

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Nonminimal roots in homotopy trees

Micheal Neal Dyer

Vol. 80 (1979), No. 2, 371–380
Abstract

Let π be a finite group which does not satisfy the Eichler condition and let M be a π-module. A π-module Mis a noncancellation example of M if M ()2M′⊕ ()2 but MM. This note classifies the set 𝒩𝒞M(π) of isomorphism classes of noncancellation examples for M = Z , where Z is the trivial π-module, M = A(π), the augmentation ideal, and M = Zπ∕(N), where (N) is the ideal generated by the norm element N = xπx. It is shown that these noncancellation examples yield nonminimal roots of the homotopy tree HT(π,m) of (π,m)-complexes.

Mathematical Subject Classification 2000
Primary: 57M20
Secondary: 16A26
Milestones
Received: 13 November 1975
Revised: 1 February 1978
Published: 1 February 1979
Authors
Micheal Neal Dyer