Malcev presentations for subsemigroups of direct products of coherent groups
نویسندگان
چکیده
منابع مشابه
Malcev presentations for subsemigroups of direct products of coherent groups
The direct product of a free group and a polycyclic group is known to be coherent. This paper shows that every finitely generated subsemigroup of the direct product of a virtually free group and an abelian group admits a finite Malcev presentation. (A Malcev presentation is a presentation of a special type for a semigroup that embeds into a group. A group is virtually free if it contains a free...
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This paper introduces and surveys the theory of Malcev presentations. [Malcev presentations are a species of presentation that can be used to define any semigroup that can be embedded into a group.] In particular, various classes of groups and monoids all of whose finitely generated subsemigroups admit finite Malcev presentations are described; closure and containment results are stated; links ...
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Let G be a finite group, F a free group of finite rank, R the kernel of a homomorphism tp of F onto G, and let [ i i , f] , [R,R] denote mutual commutator subgroups. Conjugation in F yields a G-module structure on R/[R,R]; let da[R/[R, R]) be the number of elements required to generate this module. Define d(R/[R, F]) similarly. By an earlier result of the first author, for a fixed G, the differ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2009
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2008.10.006