Some two-generator one-relator non-Hopfian groups
نویسندگان
چکیده
منابع مشابه
The Two - Generator Subgroups of One - Relator Groups with Torsion
The main aim of this paper is to show that every two-generator subgroup of any one-relator group with torsion is either a free product of cyclic groups or is a one-relator group with torsion. This result is proved by using techniques for reducing pairs of elements in certain HNN groups. These techniques not only apply to one-relator groups with torsion but also to a large number of other groups...
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...
متن کاملThe Outer Automorphism Groups of Two-generator, One-relator Groups with Torsion
The main result of this paper is a complete classification of the outer automorphism groups of two-generator, one-relator groups with torsion. To this classification we apply recent algorithmic results of Dahmani– Guirardel, which yields an algorithm to compute the isomorphism class of the outer automorphism group of a given two-generator, one-relator group with torsion.
متن کاملOn 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...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1962
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1962-10745-9