Minimal degree for a permutation representation of a classical group

1978 ◽  
Vol 30 (3) ◽  
pp. 213-235 ◽  
Author(s):  
Bruce N. Cooperstein
Keyword(s):  
Classical Group ◽  
Minimal Degree ◽  
Permutation Representation

scholarly journals On quasi-permutation representations of finite groups

1994 ◽  
Vol 36 (3) ◽  
pp. 301-308 ◽  
Author(s):  
J. M. Burns ◽  
B. Goldsmith ◽  
B. Hartley ◽  
R. Sandling
Keyword(s):  
Finite Group ◽  
Vector Space ◽  
Permutation Group ◽  
Minimal Degree ◽  
Permutation Representation ◽  
Permutation Groups ◽  
Complex Vector Space ◽  
Complex Vector ◽  
Group Situation ◽  
A Finite Group

In [6], Wong defined a quasi-permutation group of degree n to be a finite group G of automorphisms of an n-dimensional complex vector space such that every element of G has non-negative integral trace. The terminology derives from the fact that if G is a finite group of permutations of a set ω of size n, and we think of G as acting on the complex vector space with basis ω, then the trace of an element g ∈ G is equal to the number of points of ω fixed by g. In [6] and [7], Wong studied the extent to which some facts about permutation groups generalize to the quasi-permutation group situation. Here we investigate further the analogy between permutation groups and quasipermutation groups by studying the relation between the minimal degree of a faithful permutation representation of a given finite group G and the minimal degree of a faithful quasi-permutation representation. We shall often prefer to work over the rational field rather than the complex field.

Prolonging Nerve Grafts Using Chemical Extracted Muscle-in-vein with Vein Window Method Chemical acellular nerve grafts

2018 ◽  
Vol 68 (12) ◽  
pp. 2936-2940
Author(s):  
Irina Mihaela Jemnoschi Hreniuc ◽  
Camelia Tamas ◽  
Sorin Aurelian Pasca ◽  
Bogdan Ciuntu ◽  
Roxana Ciuntu ◽  
...  
Keyword(s):  
Classical Group ◽  
Donor Site ◽  
Good Alternative ◽  
Nerve Graft ◽  
Male Rats ◽  
Chemical Extraction ◽  
Nerve Grafting ◽  
Nerve Grafts ◽  
Local Resources ◽  
Window Method

Nerve injuries are a common pathology in hand trauma. The consequences are drastic both for patients and doctors/medical system. In many cases direct coaptation is impossible. A nerve graft should be used in the case of a neuroma, trauma or tumor, for restoration of nervous influx. The aim of this study is demonstrate that by grafting restant nerve stumps with muscle-in-vein nerve grafts we obtain good result in terms of functional and sensibility recovery and also our method �window-vein� is a good way of prolonging nerve grafts. The method of study is experimental. We worked in the laboratory in optimal conditions for carrying out of muscles-in-vein nerve grafts (nerve grafts size 1.5 cm-3 cm). We used acellular muscle grafts with the chemical extraction method.The study was conducted on experimental animals (Wistar male rats).We used 30 experience animals in 3 equal groups (classical group and muscle-in-vein nerve grafts-2 nerve grafts of 1,5 cm central sutured and the third group with muscle-in-vein nerve grafts, window-vein method, 3 cm). At 4 and respectively 6 weeks postoperative at the quality tests we observed the progress with the footprint test. The operated hind in comparison with the healthy hind was 86% recovered and similar with classic nerve grafts. Quantitatively the number of regenerated axons in the group with muscle-in-vein nerve grafts was significant bigger in comparison with the classical group (15%).The method using muscle-in-vein nerve graft with windows-vein it�s a good alternative for nerve grafting in comparison with classical nerve grafting. When the local possibilities are limited, this method is good for prolonging the grafts. The relationship between cost and benefit in this case it�s an advantage because we use the local resources of the affected area. The motor results of nerve grafting ingroup 2 in comparison with group 3 were similar and in some cases better in group 1. Grafting with MVNG offers a better alternative for donor site regeneration in comparison with classical nerve grafts. This method is useful to prolong nerve grafts without adding morbidity.

What sort of representation is conscious?

2002 ◽  
Vol 25 (3) ◽  
pp. 336-337 ◽  
Author(s):  
Zoltan Dienes ◽  
Josef Perner
Keyword(s):  
Mental Representations ◽  
Minimal Degree ◽  
Central Claim

We consider Perruchet & Vinter's (P&V's) central claim that all mental representations are conscious. P&V require some way of fixing their meaning of representation to avoid the claim becoming either obviously false or unfalsifiable. We use the framework of Dienes and Perner (1999) to provide a well-specified possible version of the claim, in which all representations of a minimal degree of explicitness are postulated to be conscious.

scholarly journals FINDING THE LIMIT OF INCOMPLETENESS I

2020 ◽  
Vol 26 (3-4) ◽  
pp. 268-286
Author(s):  
YONG CHENG
Keyword(s):  
Model Theory ◽  
Recursion Theory ◽  
Minimal Degree ◽  
Incompleteness Theorem ◽  
Turing Degree ◽  
Turing Reducibility ◽  
Inseparable Pair

AbstractIn this paper, we examine the limit of applicability of Gödel’s first incompleteness theorem ($\textsf {G1}$ for short). We first define the notion “$\textsf {G1}$ holds for the theory $T$”. This paper is motivated by the following question: can we find a theory with a minimal degree of interpretation for which $\textsf {G1}$ holds. To approach this question, we first examine the following question: is there a theory T such that Robinson’s $\mathbf {R}$ interprets T but T does not interpret $\mathbf {R}$ (i.e., T is weaker than $\mathbf {R}$ w.r.t. interpretation) and $\textsf {G1}$ holds for T? In this paper, we show that there are many such theories based on Jeřábek’s work using some model theory. We prove that for each recursively inseparable pair $\langle A,B\rangle $, we can construct a r.e. theory $U_{\langle A,B\rangle }$ such that $U_{\langle A,B\rangle }$ is weaker than $\mathbf {R}$ w.r.t. interpretation and $\textsf {G1}$ holds for $U_{\langle A,B\rangle }$. As a corollary, we answer a question from Albert Visser. Moreover, we prove that for any Turing degree $\mathbf {0}< \mathbf {d}<\mathbf {0}^{\prime }$, there is a theory T with Turing degree $\mathbf {d}$ such that $\textsf {G1}$ holds for T and T is weaker than $\mathbf {R}$ w.r.t. Turing reducibility. As a corollary, based on Shoenfield’s work using some recursion theory, we show that there is no theory with a minimal degree of Turing reducibility for which $\textsf {G1}$ holds.

scholarly journals THE INVARIANTS FIELD OF SOME FINITE PROJECTIVE LINEAR GROUP ACTIONS

2011 ◽  
Vol 85 (1) ◽  
pp. 19-25
Author(s):  
YIN CHEN
Keyword(s):  
Finite Field ◽  
Projective Space ◽  
Vector Space ◽  
Orthogonal Group ◽  
Homogeneous Polynomial ◽  
Classical Group ◽  
Projective Group ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Projective Linear Group

AbstractLet Fq be a finite field with q elements, V an n-dimensional vector space over Fq and 𝒱 the projective space associated to V. Let G≤GLn(Fq) be a classical group and PG be the corresponding projective group. In this note we prove that if Fq (V )G is purely transcendental over Fq with homogeneous polynomial generators, then Fq (𝒱)PG is also purely transcendental over Fq. We compute explicitly the generators of Fq (𝒱)PG when G is the symplectic, unitary or orthogonal group.

scholarly journals Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 321 ◽  
Author(s):  
Mehmet Çelik ◽  
Moges Shalla ◽  
Necati Olgun
Keyword(s):  
Group Theory ◽  
Significant Role ◽  
Classical Group ◽  
Algebraic Structures ◽  
Algebraic Systems ◽  
Homomorphism Theorem ◽  
Special Cases ◽  
Isomorphism Theorems

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.

scholarly journals TRIPLE CANONICAL SURFACES OF MINIMAL DEGREE

2000 ◽  
Vol 11 (04) ◽  
pp. 553-578 ◽  
Author(s):  
MARGARIDA MENDES LOPES ◽  
RITA PARDINI
Keyword(s):  
Minimal Degree
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