Finitely Presented Subgroups of Automatic Groups and their Isoperimetric Functions
نویسندگان
چکیده
منابع مشابه
Finitely Presented Subgroups of Automatic Groups and Their Isoperimetric Functions
We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even asynchronously automatic. We can also arrange that such subgroups satisfy, at best, an exponential isoperimetric inequality.
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1.1. Baumslag's theorem has another facet. It shows that in the variety 2l of metabelian groups, every finitely generated $I-group G occurs as a subgroup of some finitely presented 2I-group G. The analogous result for the variety of all groups is a celebrated theorem of G. Higman [8] which states that a finitely generated group G is the subgroup of a finitely presented group G if, and only if, ...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 1997
ISSN: 0024-6107
DOI: 10.1112/s0024610797005395