论文信息 - The Structure of the (Outer) Automorphism Group of a Bieberbach Group

The Structure of the (Outer) Automorphism Group of a Bieberbach Group

Referring to Tits′ alternative, we develop a necessary and sufficient condition to decide whether the normalizer of a finite group of integral matrices is polycyclic-by-finite or is containing a non-Abelian free group. This result is of fundamental importance to conclude whether the (outer) automorphism group of a Bieberbach group is polycyclic-by-finite or has a non-cyclic free subgroup.

W. Malfait | Andrzej Szczepański | Wim Malfait | A. Szczepański

[1] A. Szczepański. Outer automorphism groups of Bieberbach groups. , 1996 .

[2] L. S. Charlap,et al. Compact Flat Riemannian Manifolds III: The Group of Affinities , 1973 .

[3] Holonomy groups of Bieberbach groups with finite outer automorphism groups , 1995 .

[4] Jacques Tits,et al. Free subgroups in linear groups , 1972 .

[5] C. Sah,et al. HOLONOMY OF FLAT MANIFOLDS WITH b1 = 0, II , 1986 .

[6] H. Brown,et al. Crystallographic Groups of Four-Dimensional Space , 1978 .

[7] D. Passman,et al. The algebraic structure of group rings , 1977 .

[8] H. Zassenhaus. When is the unit group of a dedekind order solvable , 1978 .

[9] On integral groups. III. Normalizers , 1973 .

[10] Jean-Pierre Serre,et al. Linear representations of finite groups , 1977, Graduate texts in mathematics.