scholarly journals A Finite Presentation of CNOT-Dihedral Operators

2018 ◽  
Vol 266 ◽  
pp. 84-97 ◽  
Author(s):  
Matthew Amy ◽  
Jianxin Chen ◽  
Neil J. Ross
Keyword(s):  
Finite Presentation

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 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

Finite Presentation of Abelian-by-Finite-Dimensional Lie Algebras

1999 ◽  
Vol 60 (1) ◽  
pp. 45-57 ◽  
Author(s):  
R. M. Bryant ◽  
J. R. J. Groves
Keyword(s):  
Lie Algebras ◽  
Finite Presentation ◽  
Finite Dimensional ◽  
Finite Dimensional Lie Algebras

scholarly journals APPLICATIONS OF p-DEFICIENCY AND p-LARGENESS

2011 ◽  
Vol 21 (04) ◽  
pp. 547-574 ◽  
Author(s):  
J. O. BUTTON ◽  
A. THILLAISUNDARAM
Keyword(s):  
Finite Index ◽  
Coxeter Groups ◽  
Index Subgroup ◽  
Finitely Generated ◽  
P Deficiency ◽  
Finite Presentation ◽  
Finite Index Subgroup ◽  
Finitely Presented

We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is Golod–Shafarevich, and has a finite index subgroup which is Golod–Shafarevich for the remaining primes. We also generalize a result of Grigorchuk on Coxeter groups to odd primes.

scholarly journals On an Enriques Surface Associated With a Quartic Hessian Surface

2019 ◽  
Vol 71 (1) ◽  
pp. 213-246 ◽  
Author(s):  
Ichiro Shimada
Keyword(s):  
Automorphism Group ◽  
Universal Cover ◽  
Enriques Surface ◽  
Elliptic Fibrations ◽  
Double Points ◽  
Finite Presentation

AbstractLet $Y$ be a complex Enriques surface whose universal cover $X$ is birational to a general quartic Hessian surface. Using the result on the automorphism group of $X$ due to Dolgachev and Keum, we obtain a finite presentation of the automorphism group of $Y$. The list of elliptic fibrations on $Y$ and the list of combinations of rational double points that can appear on a surface birational to $Y$ are presented. As an application, a set of generators of the automorphism group of the generic Enriques surface is calculated explicitly.

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