The probability of generating a finite classical group

1990 ◽  
Vol 36 (1) ◽  
Author(s):  
WilliamM. Kantor ◽  
Alexander Lubotzky
Keyword(s):  
Classical Group ◽  
Finite Classical Group

On the Genus of a Finite Classical Group

1997 ◽  
Vol 29 (2) ◽  
pp. 159-164
Author(s):  
Martin W. Liebeck ◽  
Chris Wayman Purvis
Keyword(s):  
Classical Group ◽  
Finite Classical Group

The Steinberg Character of Finite Classical Groups

2013 ◽  
Vol 20 (01) ◽  
pp. 163-168
Author(s):  
Xueling Song ◽  
Yanjun Liu
Keyword(s):  
Classical Group ◽  
Classical Groups ◽  
Characteristic P ◽  
Combinatorial Objects ◽  
Finite Classical Group ◽  
Finite Classical Groups ◽  
Steinberg Character

Let G be a finite classical group of characteristic p. In this paper, we give an arithmetic criterion of the primes r ≠ p, for which the Steinberg character lies in the principal r-block of G. The arithmetic criterion is obtained from some combinatorial objects (the so-called partition and symbol).

MINIMAL IRREDUCIBILITY AND THE UNIPOTENT CHARACTERS OF GROUPS OF TYPE Bm AND Cm

2009 ◽  
Vol 08 (03) ◽  
pp. 413-451
Author(s):  
L. DI MARTINO ◽  
M. A. PELLEGRINI ◽  
TH. WEIGEL
Keyword(s):  
Classical Group ◽  
Proper Subgroup ◽  
Type B ◽  
Finite Classical Group

In this paper we prove that the (non-trivial) irreducible complex unipotent characters of a finite classical group G of type Bm or Cm in odd characteristic are reducible over any proper subgroup of G, apart from very few notable exceptions.

scholarly journals Lattices Generated by Two Orbits of Subspaces under Finite Singular Symplectic Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xuemei Liu
Keyword(s):  
Classical Group ◽  
Symplectic Space ◽  
Symplectic Groups ◽  
Characteristic Polynomials ◽  
Finite Classical Group

In the paper titled “Lattices generated by two orbits of subspaces under finite classical group” by Wang and Guo. The subspaces in the lattices are characterized and the geometricity is classified. In this paper, the result above is generalized to singular symplectic space. This paper characterizes the subspaces in these lattices, classifies their geometricity, and computes their characteristic polynomials.

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.

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 ON REGULAR GROUPS AND FIELDS

2014 ◽  
Vol 79 (3) ◽  
pp. 826-844 ◽  
Author(s):  
TOMASZ GOGACZ ◽  
KRZYSZTOF KRUPIŃSKI
Keyword(s):  
Conjugacy Class ◽  
Classical Group ◽  
Multiplicative Group ◽  
Finite Extension ◽  
Generic Type ◽  
Common Generalization ◽  
Counter Example ◽  
Minimal Groups ◽  
Unbounded Orbit

AbstractRegular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. LetKbe a regular field which is not generically stable and letpbe its global generic type. We observe that ifKhas a finite extensionLof degreen, thenP(n)has unbounded orbit under the action of the multiplicative group ofL.Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique nontrivial conjugacy class, and we notice that a classical group with one nontrivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then, we construct a group of cardinality ω1with only one nontrivial conjugacy class and such that the centralizers of all nontrivial elements are countable.

Preliminary Results of ‘Liver-First' Reverse Management for Advanced and Aggressive Synchronous Colorectal Liver Metastases: A Propensity-Matched Analysis

2015 ◽  
Vol 32 (1) ◽  
pp. 16-22 ◽  
Author(s):  
Kuniya Tanaka ◽  
Takashi Murakami ◽  
Kenichi Matsuo ◽  
Yukihiko Hiroshima ◽  
Itaru Endo ◽  
...  
Keyword(s):  
Liver Metastases ◽  
Colorectal Liver Metastases ◽  
Classical Group ◽  
Tumor Burden ◽  
Oncologic Outcomes ◽  
Colorectal Metastases ◽  
Second Resection ◽  
Freedom From Disease ◽  
Synchronous Colorectal Liver Metastases ◽  
Recurrence Sites

Background: Although a ‘liver-first' approach recently has been advocated in treating synchronous colorectal metastases, little is known about how results compare with those of the classical approach among patients with similar grades of liver metastases. Methods: Propensity-score matching was used to select study subjects. Oncologic outcomes were compared between 10 consecutive patients with unresectable advanced and aggressive synchronous colorectal liver metastases treated with the reverse strategy and 30 comparable classically treated patients. Results: Numbers of recurrence sites and recurrent tumors irrespective of recurrence sites were greater in the reverse group then the classic group (p = 0.003 and p = 0.015, respectively). Rates of freedom from recurrence in the remaining liver and of freedom from disease also were poorer in the reverse group than in the classical group (p = 0.009 and p = 0.043, respectively). Among patients treated with 2-stage hepatectomy, frequency of microvascular invasion surrounding macroscopic metastases at second resection was higher in the reverse group than in the classical group (p = 0.011). Conclusions: Reverse approaches may be feasible in treating synchronous liver metastases, but that strategy should be limited to patients with less liver tumor burden.

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