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Finite Presentability of Bruck–Reilly Extensions of Groups

✍ Scribed by Isabel M Araújo; N Rus̆kuc

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
96 KB
Volume
242
Category
Article
ISSN
0021-8693

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✦ Synopsis

The purpose of this paper is to consider finite generation and finite presentabil-Ž . ity of a Bruck᎐Reilly extension S s BR G, of a group G with respect to an endomorphism . It is proved that S is finitely generated if and only if G can be generated by a set of the form D ϱ A i , where A : G is finite. The main result is 0 states that S is finitely presented if and only if G can be defined by a presentation

finite set of relations R. Finally, it is proved that S is finitely presented as an inverse monoid if and only if it is finitely presented as an ordinary monoid.

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