Displaying similar documents to “Rings of Fricke Characters and Automorphism Groups of Free Groups.”

Units in group rings of crystallographic groups

Karel Dekimpe (2003)

Fundamenta Mathematicae

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In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some special classes of crystallographic groups. For a first class of groups we obtain a normal complement for the group inside the group of normalized units. For a second class of groups we show that the Zassenhaus conjectures ZC1 and ZC3 are valid. This generalizes the results known for the...

Finite-finitary, polycyclic-finitary and Chernikov-finitary automorphism groups

B. A. F. Wehrfritz (2015)

Colloquium Mathematicae

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If X is a property or a class of groups, an automorphism ϕ of a group G is X-finitary if there is a normal subgroup N of G centralized by ϕ such that G/N is an X-group. Groups of such automorphisms for G a module over some ring have been very extensively studied over many years. However, for groups in general almost nothing seems to have been done. In 2009 V. V. Belyaev and D. A. Shved considered the general case for X the class of finite groups. Here we look further at the finite case...