Exponential genus problems in one-relator products of groups
نویسندگان
چکیده
منابع مشابه
Exponential Genus Problems in One–relator Products of Groups
Exponential equations in free groups were studied initially by Lyndon and Schützenberger [26] and then by Comerford and Edmunds [5]. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper we show that for finite systems of quadratic exponential equations...
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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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We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a pushout involving a generalized triangle group. Using the theory of generalized triangle groups, we extend the range of conditions under which a number of results for one-relator products of groups, such as the...
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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...
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A recent result of D. J. Collins states that the intersection of two Magnus subgroups in a one-relator group consists either just of the ‘obvious’ intersection, or exceptionally of the free product of the obvious intersection with a free group of rank 1. In this paper, Collins’ result is generalised to apply to one-relator products of arbitrary locally-indicable groups. Moreover, a precise anal...
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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2007
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/0873