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Sebahattin Ikikardes Recep Sahin I. Naci Cangul 《Bulletin of the Brazilian Mathematical Society》2009,40(4):479-494
In this paper, first, we determine the quotient groups of the Hecke groups H(λ
q
), where q ≥ 7 is prime, by their principal congruence subgroups H
p
(λ
q
) oflevel p, where p is also prime. We deal with the case of q = 7 separately, because of its close relation with the Hurwitz groups. Then, using the obtained results, we find the principal
congruence subgroups of the extended Hecke groups $
\overline H
$
\overline H
(λ
q
) for q ≥ 5 prime. Finally, we show that some of the quotient groups of the Hecke group H(λ
q
) and the extended Hecke group $
\overline H
$
\overline H
(λ
q
), q ≥ 5 prime, by their principal congruence subgroups H
p
(λ
q
) are M*-groups. 相似文献
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Mong-Lung Lang Ser-Peow Tan 《Proceedings of the American Mathematical Society》1999,127(11):3131-3140
Let cos and let be the Hecke group associated to . In this article, we show that for a prime ideal in , the congruence subgroups of are self-normalized in .
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Frank Williams Robert J. Wisner 《Proceedings of the American Mathematical Society》1998,126(5):1331-1336
In this note we compute the integral cohomology groups of the subgroups of and the corresponding subgroups of its quotient, the classical modular group,
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Let . Let be an ideal of and let be the maximal ideal of such that . Then . In particular, if is square free, then is self-normalized in .
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Congruence subgroups of Hecke groups 总被引:1,自引:0,他引:1
Hecke groups are an important tool in subgroups of Hecke groups play an important rule investigating functional equations, and congruence in research of the solutions of the Dirichlet series. When q, m are two primes, congruence subgroups and the principal congruence subgroups of level m of the Hecke group H(√q) have been investigated in many papers. In this paper, we generalize these results to the case where q is a positive integer with q ≥ 5, √q ¢ Z and m is a power of an odd prime. 相似文献
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In this paper we address the issue of existence of newforms among the cusp forms for almost simple Lie groups using the approach of the second author combined with local information on supercuspidal representations for p-adic groups known by the first author. We pay special attention to the case of \(SL_M({\mathbb {R}})\) where we prove various existence results for principal congruence subgroups. 相似文献
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Helmut Siemon 《Journal of Geometry》1984,23(1):83-93
In the affine plane over a Galois field GF(q), q ; 3(4), q = p, of congruence transformations, of motions and of the generation of all point reflections respectively. Then we determine the groups AutC, AutM, AutM and obtain the following results: 1. Aut C is isomorphic to the product of the augmented group of similarities (generated by similarities, quasi reflections, quasi rotations 2) and the group of collineations which are induced by the automorphism of GF(q) operating on the coordinates. 2. AutM– AutC. 3. AutM– group of affinities of the affine space of dimension 2 over the prime field. 4. Moreover for any desarguesian affine plane Aut Dil (Dil = group of dilatations) is isomorphic to (the full collineation group).Lecture delivered at the Haifa Geometry conference 1983In my lecture I called these transformations semi-. To avoid confusion I follow here a suggestion of E. Schröder. 相似文献
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Andrew Putman 《Inventiones Mathematicae》2015,202(3):987-1027
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David Rosen 《Archiv der Mathematik》1986,46(6):533-538
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Kathleen L. Petersen 《Mathematische Annalen》2007,338(2):249-282
We show that there are only finitely many maximal congruence subgroups of the Bianchi groups such that the quotient by has only one cusp. 相似文献
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We study the detailed structure of a finite group under the assumption that all minimal subgroups of the generalized Fitting subgroup of some normal subgroup of are well-suited in .
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半正规n-极大子群对有限群结构的影响 总被引:1,自引:0,他引:1
设△↓n(G)为有限群G的n次极大子群的全体。1.若△↓4(G)中的子群均在G中半正规,则下述结论之一成立:(1)G是可解群;(2)G/φ(G)=A5,(3)G/φ(G)=PSL(2,13);(4)G/φ(G)=PSL(2,p),满足p=4p1 1=6p2-1,这里p1≥43,p2≥29;(5)G/φ(G)=PSL(2,p),满足p=6p1 1=4p2-1,这里p1≥7,p2≥11.2。2.设3不属于π(G),若△↓(G)中的子群均在G中半正规,则G是可解群,或G/φ(G)=Sz(2^3). 相似文献