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

B. A. F. Wehrfritz (2015)

Colloquium Mathematicae

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 but our main...

Fixed points of endomorphisms of certain free products

Pedro V. Silva (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.

Fixed points of endomorphisms of certain free products

Pedro V. Silva (2012)

RAIRO - Theoretical Informatics and Applications

The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.

Fractal representation of the attractive lamination of an automorphism of the free group

Pierre Arnoux, Valérie Berthé, Arnaud Hilion, Anne Siegel (2006)

Annales de l’institut Fourier

In this paper, we extend to automorphisms of free groups some results and constructions that classically hold for morphisms of the free monoid, i.e., the so-called substitutions. A geometric representation of the attractive lamination of a class of automorphisms of the free group (irreducible with irreducible powers (iwip) automorphisms) is given in the case where the dilation coefficient of the automorphism is a unit Pisot number. The shift map associated with the attractive symbolic lamination...

Homomorphisms from the unitary group to the general linear group over complex number field and applications

Chong-Guang Cao, Xian Zhang (2002)

Archivum Mathematicum

Let M n be the multiplicative semigroup of all n × n complex matrices, and let U n and G L n be the n –degree unitary group and general linear group over complex number field, respectively. We characterize group homomorphisms from U n to G L m when n > m ≥ 1 or n = m ≥ 3 , and thereby determine multiplicative homomorphisms from U n to M m when n > m ≥ 1 or n = m ≥ 3 . This generalize Hochwald’s result in [Lin. Alg. Appl.  212/213:339-351(1994)]: if f : U n → M n is a spectrum–preserving multiplicative homomorphism, then there exists a matrix R in G L n such that f ( A ) = R A R for...

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