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):  

1991 ◽  
Vol 01 (03) ◽  
pp. 339-351
Author(s):  
ROBERT H. GILMAN

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.



1970 ◽  
Vol 22 (5) ◽  
pp. 1079-1081 ◽  
Author(s):  
Stephen S. Shatz

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.



2013 ◽  
Vol 156 (1) ◽  
pp. 115-121
Author(s):  
ANITHA THILLAISUNDARAM

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.



2003 ◽  
Vol 181 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Gilbert Baumslag ◽  
Martin R. Bridson ◽  
Derek F. Holt ◽  
Charles F. Miller III


2013 ◽  
Vol 135 (4) ◽  
pp. 891-933 ◽  
Author(s):  
Martin R. Bridson ◽  
James Howie ◽  
Charles F. Miller ◽  
Hamish Short




2011 ◽  
Vol 21 (04) ◽  
pp. 547-574 ◽  
Author(s):  
J. O. BUTTON ◽  
A. THILLAISUNDARAM

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.



2019 ◽  
Vol 71 (1) ◽  
pp. 213-246 ◽  
Author(s):  
Ichiro Shimada

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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