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3 edition of subgroups of the generalized finite modular group found in the catalog.

subgroups of the generalized finite modular group

Eliakim Hastings Moore

# subgroups of the generalized finite modular group

## by Eliakim Hastings Moore

• 259 Want to read
• 18 Currently reading

Published by University of Chicago Press in Chicago .
Written in English

Subjects:
• Group theory.

• Edition Notes

Printed from First series, v. 9 (p. 141-190) of the Decennial publications of the University of Chicago.

Classifications The Physical Object Statement by Eliakim Hastings Moore. LC Classifications QA271 .M82 Pagination 52 p. Number of Pages 52 Open Library OL6941584M LC Control Number 04015385 OCLC/WorldCa 4389656

Generalized fullerene-like lattices, and itinerant interacting electrons The construction is based on a hierarchy of finite, finitely presented groups derived from subgroups of the modular group. The infinite lattices obtainable are schwartzite-like tubular structures. The Hubbard model is then discussed, in the three most commonly adopted. Generalized quaternion groups 12 2-Groups without non-cyclic abelian characteristic subgroups 15 Transfer and fusion of elements 25 Coprime group actions 34 Simple groups with dihedral or semi-dihedral Sylow 2-subgroups 38 Simple groups with strongly embedded subgroups 40 2 Group representations and character theory

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. We define generalized Frobenius-Schur indicators for objects in a linear pivotal category C. An equivariant indicator of an object is defined as a functional on the Grothendieck algebra of the quantum double Z(C) of C using the values of the generalized Frobenius-Schur indicators. ALL FINITE GENERALIZED TRIANGLE GROUPS L. LEVAI, G. ROSENBERGER, AND B. SOUVIGNIER Abstract. We complete the classification of those generalized triangle groups that are finite. INTRODUCTION A generalized triangle group is one given by a presentation (a, b\ap = bq = Rm = 1), where p, q, m are integers greater than 1, and R is a word of the.

Given a finite modular tensor category, we associate with each compact surface with boundary a cochain complex in such a way that the mapping class group of the surface acts projectively on its. Let σ={σi|i∈I} be a partition of the set of all primes P and G a finite group. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠1 of H is a Hall σi.

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### Subgroups of the generalized finite modular group by Eliakim Hastings Moore Download PDF EPUB FB2

Subgroups of the generalized finite modular group. Chicago, University of Chicago Press, (OCoLC) Document Type: Book: All Authors / Contributors: Eliakim Hastings Moore.

"The monumental classification of finite simple groups, which occupies s pages spread over journal articles, is now complete, and the complete list of the finite simple groups has attracted wide Atlas brings together detailed information about these groups--their construction, character tables, maximal subgroups, and prefatory material is as clear and 5/5(1).

In this paper, we give some new conditions under which a normal subgroup E of a finite group G is hypercyclically embedded in G, that is, every chief factor of G below E is cyclic. Keywords: Finite group, generalized m-S-permutable subgroup, hypercyclically embedded subgroup, modular subgroup, m-S-permutable subgroupAuthor: Jianhong Huang, Bin Hu.

In this chapter the questions and results of the first chapter for the homogeneous and inhomogeneous modular group will be carried over and extended to its subgroups.

We will restrict ourselves mainly to subgroups of finite index, and turn our particular interest to a special class of subgroups, the so-called congruence : Bruno Schoeneberg.

Abstract. Let G be a finite group and H a subgroup of say that H: is generalized S-quasinormal in G if $$H=\left\langle A,B\right\rangle$$ for some modular subgroup A and S-quasinormal subgroup B of G; m-S-complemented in G if there are a generalized S-quasinormal subgroup S and a subgroup T of G such that $$G=HT$$ and $$H\cap T\le S\le H$$.In this paper, we study finite groups Author: Khaled A.

Al-Sharo. multiple of 6 (see [3] or [6]) and there are only finitely many normal subgroups of r of a given finite index p, since the total number of subgroups of a given finite index in a finitely generated group is finite.

The purpose of this article is to obtain some information about the function N{p), the number of normal subgroups of T of index p. Chapter Galois groups and congruence subgroups Abstract We prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear.

If the action is only projective, we show that the projective kernel is a congruence subgroup. Modular abelian varieties of odd modular degree Yazdani, Soroosh, Algebra & Number Theory, A generalization of modular forms Haque, Adam, Involve: A Journal of Mathematics, Necessary Fredholm conditions for weighted singular integral operators with shifts and slowly oscillating data Karlovich, Alexei Yu., Karlovich, Yuri I., and Lebre.

groups whose orders are divisible by ps, ps and p* was given by R. Borger.* As a result of the determination of the ternary modular groups in this paper, the subgroups of the two systems of simple groups, LF(3, pk) and HO{ §,p°c), are found in the cases where p is an odd prime, f The LF(3, pk) is the group.

In the lists of subgroups, the trivial group and the group itself are not listed. Where there are several isomorphic subgroups, the number of such subgroups is indicated in parentheses. List of small abelian groups. The finite abelian groups are either cyclic groups, or direct products thereof; see abelian groups.

Important subgroups of the modular group Γ, called congruence subgroups, are given by imposing congruence relations on the associated matrices.

There is a natural homomorphism SL (2, Z) → SL (2, Z/NZ) given by reducing the entries modulo N. This induces a homomorphism on the modular group PSL (2, Z) → PSL (2, Z/NZ).

Let G be a finite group and H a subgroup of G. We say that H: is generalized S-quasinormal in G if $$H=\left\langle A,B\right\rangle$$ for some modular subgroup A and S-quasinormal subgroup B of.

In mathematics, a topological group is a group G together with a topology on G such that both the group's binary operation and the function mapping group elements to their respective inverses are continuous functions with respect to the topology.

A topological group is a mathematical object with both an algebraic structure and a topological structure. Thus, one may perform algebraic operations. The principal theme of this paper is the enumeration of finite index subgroups Δ in a free product Γ of finite groups under various restrictions on the isomorphism type of particular, we completely resolve the realization, asymptotic, and distribution problems for free products Γ of cyclic groups of prime order (prior to this work, these questions were wide open even in the case of.

Specifically, groups 1a, 1b, 2, 3, 4a and 6 are known to be finite of the given orders [14, 17], while group 4b was shown to contain non-abelian free subgroups in [20] (by observing that its.

Dr Gagen presents a simplified treatment of recent work by H. Bender on the classification of non-soluble groups with abelian Sylow 2-subgroups, together with some background material of wide interest. The book is for research students and specialists in group theory and allied subjects such as finite.

$\begingroup$ This OEIS link is essentially about the number of minimal subgroups of the symmetric groups. The question, however, is about the structure (not just the number) of maximal (not minimal) subgroups of finite simple groups (not the symmetric groups).

$\endgroup$ – Andreas Blass Nov. General linear group of a vector space. If V is a vector space over the field F, the general linear group of V, written GL(V) or Aut(V), is the group of all automorphisms of V, i.e. the set of all bijective linear transformations V → V, together with functional composition as group V has finite dimension n, then GL(V) and GL(n, F) are isomorphic.

A subgroup H of a group G is commensurable (or close) to a normal subgroup if there is a normal subgroup N of G such that the index | H N: (H ∩ N) | is finite; if further the subgroup N can be chosen to be contained in H, i.e. if H / H G is finite, then H is called describe the structure of (generalized) soluble groups satisfying the weak minimal condition on subgroups that.

The monster has at least 44 conjugacy classes of maximal -abelian simple groups of some 60 isomorphism types are found as subgroups or as quotients of subgroups.

The largest alternating group represented is A The monster contains 20 of the 26 sporadic groups as subquotients. This diagram, based on one in the book Symmetry and the Monster by Mark Ronan.

Abstract. Let p and q be integers such that 2 ≤ p ≤ q; p + q > 4 and let H p,q be the generalized Hecke group associated to p and q: The generalized Hecke group Hp,q is generated by X(z) = -(z-λ p)-1 and Y (z) = -(z+ λ q)-1 where λ p = 2 cos ≤ π/p and λ q = 2 cos π/q.

The extended generalized Hecke group H̅ p,q is obtained by adding the reection R(z) = 1/z̅ to the generators of. The set of all equivariant indicators admits a natural action of the modular group. Using the properties of equivariant indicators, we prove a congruence subgroup theorem for modular categories.

As a consequence, all modular representations of a modular category have finite images, and they satisfy a conjecture of Eholzer.Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share .