D. Gorenstein, "Finite Groups", Second edition, Chelsea Publishing Co., New York, 1980. Home/Search Document Not in Database Summary Related Articles Check |
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Linear Differential Operators for Polynomial Equations - Cormier, Singer, Trager.. (Correct)
.... , y s 1 of k 0 (x) y 1 , y s ) y s 1 ) over k 0 (x) y 1 , y s ) where # N is such that # m(m s 1) is the order of G k 0 (x) In particular for s = 1 this includes the case where G k0 (x) is a Frobenius group, for s = 2 this includes the Zassenhaus groups [17] and for s = m s = m 2 this includes the symmetric group Sm and the alternating group Am . Proof: We proceed by induction. Let s = 1. Since G k0 (x) is transitive a basis of k 0 (x) y 1 ) k 0 (x) is . Let y 2 y 1 be a second root of P and denote # It is important to note that those ....
D. Gorenstein, (1968). Finite Groups, Harper & Row, New York-London,
Dynamics Of Finite Semigroups - Almeida (2001) (Correct)
....3) Sz(2 r ) 1) where p, q and r are primes such that p is di erent from 3 and is either 5 or congruent with 2 mod 5, and r is odd. Here, PSL(n; q l ) denotes the projective special linear group in dimension n over the Galois eld GF(q l ) and Sz(2 r ) denote the Suzuki groups (see [9]) Calculations on any speci c such group (with not too large parameters) show that it fails u = 1 but no pattern for a good evaluation seems to emerge. Such calculations add further evidence for Plotkin s conjecture but fall short of proving it. 3 Dynamics of implicit operators In general, ....
D. Gorenstein, Finite Groups, Harper & Row, New York, 1968.
Linear Differential Operators for Polynomial Equations - Cormier, Ulmer, Singer (Correct)
.... ; y 1 s 1 g of k 0 (x) y 1 ; y s ) y s 1 ) over k 0 (x) y 1 ; y s ) where 2 N is such that m(m 1) m s 1) is the order of G k0 (x) In particular for s = 1 this includes the case where G k0 (x) is a Frobenius group, for s = 2 this includes the Zassenhaus groups [11] and for s = m 1 and s = m 2 this includes the symmetric group Sm and the alternating group Am . Proof. We proceed by induction. Let s = 1. Since G k0 (x) is transitive a basis of k 0 (x) y 1 ) k 0 (x) is f1; y 1 ; y m 1 1 g. Let y 2 6= y 1 be a second root of P and denote K the ....
D. Gorenstein. Finite Groups. Harper& Row, New York, 1968.
Cubic Semisymmetric Graphs of Order 2p³ - Malnic, Marusic, Wang (2000) (Correct)
....cubic semisymmetric graph of order 2p 3 , where p 3 is a prime. 3 1 Introduction Throughout this paper graphs are assumed to be finite, and, unless specified otherwise, simple, undirected and connected. For the group theoretic concepts and notation not defined here we refer the reader to [3, 9, 21]. Given a graph X we let V (X) E(X) and AutX be the vertex set, the edge set and the automorphism group of X, respectively. For two adjacent vertices u and v we write u v, and use the symbol uv to denote either the edge between u and v, or the arc from u to v. No ambiguity should arise for we ....
D. Gorenstein, "Finite Groups", Harper and Row, New York, 1968.
Computing the Galois Group of a Polynomial Using Linear.. - Cormier, Singer, Ulmer (Correct)
.... 1 ; y s ) y s 1 ) over Q(x) y 1 ; y s ) where 2 N is such that Delta m(m Gamma 1) Delta Delta Delta (m Gamma s 1) is the order of GQ (x) In particular for s = 1 this includes the case where GQ (x) is a Frobenius group, for s = 2 this includes the Zassenhaus groups [7] and for s = m Gamma 1 and s = m Gamma 2 this includes the symmetric group Sm and the alternating group Am . Cormier, Singer, Ulmer: Computing the Galois Group of a Polynomial 18 Proof: We proceed by induction. Let s = 1. Since GQ (x) is transitive a basis of Q(x) y 1 ) Q(x) is f1; y 1 ; ....
D. Gorenstein. Finite Groups. Harper& Row, New York, 1968.
The Primitive p-Frobenius Groups - Fleischmann, Lempken, Tiep (1997) (Correct)
....p. iii) 3 6 : SL 2 (13) 2 F(3) Hering s group) iv) 7 8 : 2 1 4 Gamma nA 5 ) 2 F(2) and 7 4 : SL 2 (9) 5 12 : SL 2 (13) 2 F(3) The following result will be used in the next chapter. Theorem 2.3 Let G be a finite group with a nilpotent maximal subgroup H. i) Thompson; see [4], Thm. 10.3.2] If H has odd order then G is solvable. ii) Baumann; see [1] If G is non solvable then O 2 (G=F (G) is a direct product of simple groups isomorphic to L 2 (q) with primes q of the form 2 n Sigma 1 or q = 9. We will also need the following result, which is an easy ....
....G 2 F na (p) Suppose in addition that G ff is not a p group. Then we can find x 2 G ff of prime order q 6= p. Now for any 1 6= y 2 R, G ff G y(ff) is a p group. In 6 particular, x y 62 G ff , so y x 6= y and x acts fixed point freely on Rnf1g. By a well known theorem of Thompson (cf. [4] Thm. 10.2.1) R must be nilpotent, a contradiction. Thus G ff must be a p group. By 1) G ff 2 Syl 2 (G) and jRj = G : G ff ] is odd. So R (and G = R Delta G ff ) is solvable, again a contradiction. 3) The claims concerning S now follow immediately. Furthermore, if G ff is a p group, then (i) ....
D. Gorenstein, "Finite Groups", Harper and Row, 1968.
PSL(3,q) and PSU(3,q) on PROJECTIVE PLANES OF ORDER q^4 - Moorhouse (Correct)
....results contained herein were contained in the author s doctoral thesis [27] under the kind supervision of Professor Chat Y. Ho. 2. NOTATION AND PRELIMINARIES Most of our notation and terminology is standard. Some better known results are stated below without proof and the reader is referred to [11] for group theory, and [5] or [18] for projective planes. We denote the cyclic group of order n by C n , and the symmetric and alternating groups of degree n by S n and A n . For a finite group G we denote by G 0 the derived subgroup of G, and by Syl p (G) the class of all Sylow p subgroups of ....
Gorenstein, D., Finite Groups, Harper & Row, New York, 1968.
PSL(2,q) as a Collineation Group of Projective Planes of Small.. - Moorhouse (1989) (Correct)
....ensues and we conclude that G contains involutory homologies. I wish to thank Professor W. M. Kantor for suggestions which were helpful in revising the original manuscript. 2. NOTATION AND PRELIMINARIES Most of our notation and terminology is standard and follows [2] 11] for projective planes; [6] for finite groups. We assume some of the better known results, and in the following we omit proofs of the more accessible statements. A pair (X; l) consisting of a point X and a line l of a projective plane, is a flag or an antiflag according as X 2 l or X = 2 l. By (l) we mean the set of points ....
Gorenstein, D., Finite Groups, Harper & Row, New York, 1968.
On a theorem of Deaconescu - Bannuscher, Tiedt (1994) (Correct)
....Kolloquium, Rostock, 22. und 23. Mai 24 Wolfgang Bannuscher; Gunter Tiedt Deaconescu asks if the conditions in Theorem 1 (II) are also sufficient. In this note we show that this is not the case in generally. Furthermore we give a new characterization of CP 1 groups. 2 Result and Examples In [3] and [1] we can find a classification of all solvable CN groups and nonsolvable CP groups. From this we can easily deduce: Theorem 2 A group G is a CP group iff one of the following holds: i) G is isomorphic with PSL(2; q) with q = 4; 7; 8; 9; 17; PSL(3; 4) Sz(8) Sz(32) or M 10 . ii) G ....
Gorenstein, D. : Finite Groups. New York 1968
Bivariate factorizations via Galois theory, with application to.. - Zieve (Correct)
....Hermitian form H( q 1 1 Gamma q 1 2 . Both of these subgroups are conjugate to SU 2 (q) which is the subgroup preserving the Hermitian form q 1 1 q 1 2 . The latter conjugacy was known to Dickson [8, x144] but seems to have been forgotten over the years: it is not in [10] or [17] and is given incorrectly in [14] Specifically, Suzuki proves only that SU 2 (q) SL 2 (q) by first computing all subgroups of SL 2 (q 2 ) then noting that any such subgroup of the same order as SL 2 (q) must be isomorphic to SL 2 (q) 17, 6.22) In the proof of [14, Hilfssatz ....
D. Gorenstein, "Finite groups," Harper&Row, New York, 1968.
Designs with Block Size 6 from PSL(2, q) and Their Large Sets - Gh Omidi Pournaki (Correct)
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D. Gorenstein, "Finite Groups", Second edition, Chelsea Publishing Co., New York, 1980.
On the Monomiality of Nice Error Bases - Klappenecker, Rötteler (2003) (Correct)
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D. Gorenstein, Finite Groups, Chelsea, New York, 1980.
Automorphism Groups with Cyclic Commutator Subgroup and.. - Dobson, Gavlas, al. (1997) (Correct)
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D. Gorenstein, Finite Groups (Chelsea, New York, 1980).
Implications of Conjugacy Class Size - Camina, Camina (Correct)
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D. Gorenstein. Finite Groups. (Harper & Row, 1968).
On Subgroups of Prime Power Index - Baumeister (1997) (Correct)
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D. Gorenstein, Finite Groups, Harper & Row, New York 1968.
Maps Between Classifying Spaces Revisited - Jackowski, McClure, Oliver (Correct)
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D. Gorenstein, Finite groups, Harper & Row (1968)
Images Of Semistable Galois Representations - Ribet (1997) (Correct)
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D. Gorenstein, Finite Groups, Chelsea, New York, 1980. 296 KENNETH A. RIBET
On the generalized Fitting group of locally finite, finitary.. - Meierfrankenfeld (1996) (Correct)
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D. Gorenstein, Finite Groups, Harper, New York (1980)
Short Presentations for Finite Groups - Babai, Goodman, Kantor, Luks.. (1995) (4 citations) (Correct)
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D. Gorenstein. Finite Groups. 2nd ed., Chelsea, New York, 1980.
Fixed Point Sets And Tangent Bundles Of Actions On Disks And.. - Oliver (1 citation) (Correct)
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D. Gorenstein, Finite groups, Harper & Row (1968)
On Locally Finite Power-Commutative Groups - Wu (1998) (Correct)
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D. Gorenstein, Finite Groups, 2nd ed., Chelsea, New York, 1980.
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