scholarly journals CANCELLATIVE AND MALCEV PRESENTATIONS FOR FINITE REES INDEX SUBSEMIGROUPS AND EXTENSIONS

2008 ◽  
Vol 84 (1) ◽  
pp. 39-61 ◽  
Author(s):  
ALAN J. CAIN ◽  
EDMUND F. ROBERTSON ◽  
NIK RUŠKUC
Keyword(s):  
Cancellative Semigroup ◽  
Finite Presentation

AbstractIt is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.)

VERIFYING THAT A GROUP IS VIRTUALLY FREE

1991 ◽  
Vol 01 (03) ◽  
pp. 339-351
Author(s):  
ROBERT H. GILMAN
Keyword(s):  
Finite Index ◽  
Free Subgroup ◽  
Universal Group ◽  
Finitely Presented Groups ◽  
Finite Presentation ◽  
Finitely Presented

This paper is concerned with computation in finitely presented groups. We discuss a procedure for showing that a finite presentation presents a group with a free subgroup of finite index, and we give methods for solving various problems in such groups. Our procedure works by constructing a particular kind of partial groupoid whose universal group is isomorphic to the group presented. When the procedure succeeds, the partial groupoid can be used as an aid to computation in the group.

Finite Subsghemes of Group Schemes

1970 ◽  
Vol 22 (5) ◽  
pp. 1079-1081 ◽  
Author(s):  
Stephen S. Shatz
Keyword(s):  
Simple Proof ◽  
Group Schemes ◽  
Base Scheme ◽  
Finite Presentation ◽  
Empty Subset

If G is an ordinary group and H is a non-empty subset of G, then there are two elementary criteria for H to be a subgroup of G. The first and more general is that the mapping H × H → G × G → G, via 〈x, y〉 ⟼ xy–1 factor through H. The second is that H be finite and closed under multiplication.In the category of group schemes, if one writes down the hypotheses for the first criterion in diagram form, one can supply the proof by a suitable translation of the classical arguments. The only point that causes any difficulty whatsoever is that one must assume that the structure morphism πH: H → S (S is the base scheme) is an epimorphism in order to factor the identity section through H. The second criterion is also true for group schemes under a mild finite presentation hypothesis. It is our aim to provide a simple proof for the following theorem.

scholarly journals On the equivalence of cancellative extensions of commutative cancellative semigroups by groups

1971 ◽  
Vol 12 (2) ◽  
pp. 187-192
Author(s):  
Charles V. Heuer
Keyword(s):  
Abelian Group ◽  
Cyclic Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ideal Extension ◽  
Cancellative Semigroup ◽  
Finitely Generated ◽  
Necessary And Sufficient

In [1] D. W. Miller and the author established necessary and sufficient conditions for the existence of a cancellative (ideal) extension of a commutative cancellative semigroup by a cyclic group with zero. The purpose of this paper is to extend these results to cancellative extensions by any finitely generated Abelian group with zero and to establish in this general case conditions under which two such extensions are equivalent.

scholarly journals Cancellative semigroup rings which are Azumaya algebras

1988 ◽  
Vol 117 (2) ◽  
pp. 290-296 ◽  
Author(s):  
J Okninski ◽  
F Van Oystaeyen
Keyword(s):  
Cancellative Semigroup ◽  
Semigroup Rings ◽  
Azumaya Algebras

scholarly journals Chain conditions and semigroup graded rings

1988 ◽  
Vol 45 (3) ◽  
pp. 372-380 ◽  
Author(s):  
E. Jespers
Keyword(s):  
Inverse Semigroup ◽  
Sufficient Conditions ◽  
Cancellative Semigroup ◽  
Graded Rings ◽  
Semigroup Rings ◽  
Graded Ring ◽  
Product Group ◽  
Chain Conditions ◽  
Unique Product

AbstractThe following questions are studied: When is a semigroup graded ring left Noetherian, respectively semiprime left Goldie? Necessary sufficient conditions are proved for cancellative semigroup-graded subrings of rings weakly or strongly graded by a polycyclic-by-finite (unique product) group. For semigroup rings R[S] we also give a solution to the problem in case S is an inverse semigroup.

scholarly journals Groups of p-deficiency one

2013 ◽  
Vol 156 (1) ◽  
pp. 115-121
Author(s):  
ANITHA THILLAISUNDARAM
Keyword(s):  
Finite Index ◽  
Index Subgroup ◽  
P Deficiency ◽  
Finitely Presented Groups ◽  
Finite Presentation ◽  
Finite Index Subgroup ◽  
Finitely Presented

AbstractIn a previous paper, Button and Thillaisundaram proved that all finitely presented groups of p-deficiency greater than one are p-large. Here we prove that groups with a finite presentation of p-deficiency one possess a finite index subgroup that surjects onto the integers. This implies that these groups do not have Kazhdan's property (T). Additionally, we show that the aforementioned result of Button and Thillaisundaram implies a result of Lackenby.

scholarly journals Finite presentation of fibre products of metabelian groups

2003 ◽  
Vol 181 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Gilbert Baumslag ◽  
Martin R. Bridson ◽  
Derek F. Holt ◽  
Charles F. Miller III
Keyword(s):  
Metabelian Groups ◽  
Finite Presentation ◽  
Fibre Products

scholarly journals On the finite presentation of subdirect products and the nature of residually free groups

2013 ◽  
Vol 135 (4) ◽  
pp. 891-933 ◽  
Author(s):  
Martin R. Bridson ◽  
James Howie ◽  
Charles F. Miller ◽  
Hamish Short
Keyword(s):  
Free Groups ◽  
Finite Presentation ◽  
Subdirect Products
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