منابع مشابه
On One-relator Inverse Monoids and One-relator Groups
It is known that the word problem for one-relator groups and for one-relator monoids of the form Mon〈A ‖ w = 1〉 is decidable. However, the question of decidability of the word problem for general one-relation monoids of the form M = Mon〈A ‖ u = v〉 where u and v are arbitrary (positive) words in A remains open. The present paper is concerned with one-relator inverse monoids with a presentation o...
متن کاملAutomorphisms of One-relator Groups
It is a well-known fact that every group G has a presentation of the form G = F/R, where F is a free group and R the kernel of the natural epimorphism from F onto G. Driven by the desire to obtain a similar presentation of the group of automorphisms Aut(G), we can consider the subgroup Stab(R) ⊆ Aut(F ) of those automorphisms of F that stabilize R, and try to figure out if the natural homomorph...
متن کاملIrreducible Components in an Algebraic Variety of Representations of a Family of One-relator Groups
Given a finitely generated group G, the set Hom(G, SL2C) inherits the structure of an algebraic variety R(G) called the representation variety of G. This algebraic variety is an invariant of G. Let Gpt = 〈a, b; a p = b〉, where p, t are integers greater than one. In this paper a formula is produced yielding the number of four dimensional irreducible components of the affine algebraic variety R(G...
متن کاملConjugacy Separability of Some One-Relator Groups
Conjugacy separability of any group of the class of one-relator groups given by the presentation a, b; a m , b n 1m, n > 1 is proven. The proof made used of theoretical combinatorial group methods, namely the structure of amalgamated free products and some properties of the subgroups and quotients of any group of the class of one-relator groups given above.
متن کاملSome results on one-relator surface groups
If S is noncompact, or has nonempty boundary, then π1(S) is free, and the answer to Question 1 is yes, by an old result of Magnus [7] on one-relator groups. (Essentially, the defining relator in a one-relator group on a given generating set is unique up to conjugacy and inversion.) We will show (see Theorem 3.4 below) that Question 1 also has an affirmative answer in the case of a closed surfac...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1998
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)00123-0