论文信息 - New perspectives of the power-commutator-structure: Coclass trees of CF-groups and related BCF-groups

New perspectives of the power-commutator-structure: Coclass trees of CF-groups and related BCF-groups

Abstract. Let e ≥ 2 be an integer. Among the finite 3-groups G with bicyclic commutator quotient G/G′ ≃ C3e × C3, having one non-elementary component with logarithmic exponent e, there exists a unique pair of coclass trees with distinguished rank distribution ̺ ∼ (2, 2, 3; 3). One tree T (M (e) 1 ) consists of CF-groups with coclass e, and the other tree T e+1(M (e+1) 1 ) consists of BCF-groups with coclass e+1. It is proved that, due to a chain of periodic bifurcations, the vertices of all pairs (T ,T e+1) with e ≥ 3 can be constructed as p-descendants of the single root M (3) 1 of order 3 6 by means of the p-group generation algorithm by Newman and O’Brien.

Daniel C. Mayer | D. C. Mayer

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