By Jorge Almeida, Benjamin Steinberg (auth.), Jean-Camille Birget, Stuart Margolis, John Meakin, Mark Sapir (eds.)

ISBN-10: 1461213886

ISBN-13: 9781461213888

ISBN-10: 1461271266

ISBN-13: 9781461271260

This quantity comprises papers that are established totally on talks given at an inter nationwide convention on Algorithmic difficulties in teams and Semigroups held on the college of Nebraska-Lincoln from may possibly ll-May sixteen, 1998. The convention coincided with the Centennial occasion of the dept of arithmetic and information on the college of Nebraska-Lincoln at the party of the only hun dredth anniversary of the granting of the 1st Ph.D. by means of the dep.. investment was once supplied via the USA nationwide technology origin, the dept of Math ematics and facts, and the varsity of Arts and Sciences on the collage of Nebraska-Lincoln, in the course of the College's concentration software in Discrete, Experimental and utilized arithmetic. the aim of the convention was once to assemble researchers with pursuits in algorithmic difficulties in team conception, semigroup idea and machine technological know-how. a very helpful characteristic of this convention was once that it supplied a framework for trade of rules among the learn groups in semigroup conception and team thought, and a number of other of the papers accrued the following mirror this interac tion of principles. The papers amassed during this quantity signify a go element of the various effects and concepts that have been mentioned within the convention. They mirror a synthesis of overlapping rules and strategies encouraged by means of difficulties bearing on finite monoids, finitely offered mono ids, finitely awarded teams and unfastened groups.

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**Additional info for Algorithmic Problems in Groups and Semigroups**

**Example text**

They take the form G[X] = G[X}, ... , XII] = G * (Xl, ... , XII), 38 G. Baumslag, A. Myasnikov, V. Remeslennikov the free productofG and the free group F(X) freely generated by X = {Xl. ••• ,xn }. These G-groups can be likened to algebras over a unitary commutative ring, more specially a field, with G playing the role of the coefficient ring. • Xn • with coefficients in G. We use functional notation here, (1) thereby expressing the fact that the word representing f in G[X] involves the variables Xl, ...

We use functional notation here, (1) thereby expressing the fact that the word representing f in G[X] involves the variables Xl, ... ,Xn and, as needed, the constants gl, ... ,gm E G. 7 G-equationally Noetherian groups Let H be a G-group and let f E G[X]. , an, gl,···, gm) = 1. We sometimes say that f vanishes at v. , S vanishes at v. In this event we also say that v is an H -point of S. We denote the set of all roots of S by VH (S). So VH(S) = (v E H n I f(v) = 1 for all f E S}. Then a G-group H is called G-equationally Noetherian if for every n > 0 and every subset S of G[XI.

B, Academic Press, New York, 1976. [22] T. Evans, Some connections between residual finiteness, finite embeddability and the word problem,J. London Math. , 1 (1969), 399-403. [23] M. D. Fried and M. Jarden, FieldArithmetic, Springer-Verlag, Berlin, 1986. [24] K. Henckell, Pointlike sets: The finest aperiodic cover of a finite semigroup, J. Pure Appl. Algebra, 55 (1988), 85-126. ,Product expansions,]. PureAppl. Algebra, 101 (1995), 157-170. [25] [26] K. Henckell, S. -E. Pin, and J. Rhodes, Ash's type II theorem, profinite topology and Malcev products, part I, Internat.

### Algorithmic Problems in Groups and Semigroups by Jorge Almeida, Benjamin Steinberg (auth.), Jean-Camille Birget, Stuart Margolis, John Meakin, Mark Sapir (eds.)

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