Automorphisms of Finitely Generated Free G-Groups

Automorphisms of Free Groups Have Finitely Generated Fixed Point Sets

An automorphism of a finitely generated free group F extends to a homeomorphism of the end completion E of F. The set of fixed points of this homeomorphism is finitely generated in a certain sense. In particular this implies that the subgroup of elements fixed by the automorphism is finitely generated in the usual sense. The emphasis on E instead of F in this paper is analogous to Thurston’s st...

On finitely generated submonoids of free groups

We prove that the classes of graded monoids, regular monoids and Kleene monoids coincide for submonoids of free groups. We also prove that it is decidable whether or not a finitely generated submonoid of a free group is graded, and solve the homomorphism and isomorphism problems for graded submonoids of free groups. This generalizes earlier results for submonoids of free monoids. MSC: 20E05; 20...

Bernoulli Automorphisms of Finitely Generated Free Mv-algebras

MV-algebras can be viewed either as the Lindenbaum algebras of Lukasiewicz infinite-valued logic, or as unit intervals [0, u] of lattice-ordered abelian groups in which a strong order unit u > 0 has been fixed. They form an equational class, and the free n-generated free MV-algebra is representable as an algebra of piecewise-linear continuous functions with integer coefficients over the unit n-...

Finitely Generated Abelian Groups

Finitely Generated Semiautomatic Groups

The present work shows that Cayley automatic groups are semiautomatic and exhibits some further constructions of semiautomatic groups and in particular shows that every finitely generated group of nilpotency class 3 is semiautomatic.