scholarly journals Classification of normal subgroups of the modular group

1967 ◽  
Vol 126 (2) ◽  
pp. 267-267 ◽  
Author(s):  
Morris Newman
Keyword(s):  
Modular Group ◽  
Normal Subgroups

ON THE CLASSIFICATION OF EVEN UNIMODULAR LATTICES WITH A COMPLEX STRUCTURE

2012 ◽  
Vol 08 (04) ◽  
pp. 983-992 ◽  
Author(s):  
MICHAEL HENTSCHEL ◽  
ALOYS KRIEG ◽  
GABRIELE NEBE
Keyword(s):  
Modular Group ◽  
Complex Structure ◽  
Theta Series ◽  
Number Fields ◽  
Quadratic Number ◽  
Imaginary Quadratic Fields ◽  
Rings Of Integers ◽  
Hermitian Modular Form ◽  
Imaginary Quadratic Number

This paper classifies the even unimodular lattices that have a structure as a Hermitian [Formula: see text]-lattice of rank r ≤ 12 for rings of integers in imaginary quadratic number fields K of class number 1. The Hermitian theta series of such a lattice is a Hermitian modular form of weight r for the full modular group, therefore we call them theta lattices. For arbitrary imaginary quadratic fields we derive a mass formula for the principal genus of theta lattices which is applied to show completeness of the classifications.

scholarly journals Some maximal normal subgroups of the modular group

1987 ◽  
Vol 30 (1) ◽  
pp. 97-101
Author(s):  
Gareth A. Jones
Keyword(s):  
Finite Group ◽  
Quotient Group ◽  
Modular Group ◽  
Galois Field ◽  
Normal Subgroups ◽  
Finitely Generated ◽  
Fractional Group

For each finite group G, let G denote the set of all normal subgroups of the modular group Γ = PSL2(ℤ) with quotient group isomorphic to G; since Γ is finitely generated, the number NG = |G| of such subgroups is finite. We shall be mainly concerned with the case where G is the linear fractional group PSL2(q) over the Galois field GF(q), in which case we shall write (q) and N(q) for G and NG; for q>3, PSL2(q) is simple, so the elements of (q) will be maximal normal subgroups of Γ.

Modular Group Algebras with Small Upper Lie Nilpotency Index

2020 ◽  
Vol 12 (1) ◽  
pp. 108-111
Author(s):  
Suchi Bhatt ◽  
Harish Chandra
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Group Algebras ◽  
Modular Group Algebra ◽  
Nilpotency Index

Let KG be the modular group algebra of a group G over a field K of characteristic p > 0. The classification of group algebras KG with upper Lie nilpotency index tL(KG) greater than or equal to |G′| – 13p + 14 have already been done. In this paper, our aim is to classify the group algebras KG for which tL(KG) = |G′| – 14p + 15.

Classification of Normal Subgroups of Hecke Group H6 in Terms of Parabolic Class Number

2011 ◽  
Author(s):  
Aysun Yurttas ◽  
Musa Demirci ◽  
I. Naci Cangul ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Class Number ◽  
Normal Subgroups ◽  
Hecke Group

scholarly journals The group of endotrivial modules for the symmetric and alternating groups

2010 ◽  
Vol 53 (1) ◽  
pp. 83-95 ◽  
Author(s):  
Jon F. Carlson ◽  
David J. Hemmer ◽  
Nadia Mazza
Keyword(s):  
Modular Group ◽  
Symmetric Groups ◽  
Group Algebras ◽  
Torsion Subgroup ◽  
Alternating Groups ◽  
Free Part ◽  
Rank 2 ◽  
Torsion Free

AbstractWe complete a classification of the groups of endotrivial modules for the modular group algebras of symmetric groups and alternating groups. We show that, for n ≥ p2, the torsion subgroup of the group of endotrivial modules for the symmetric groups is generated by the sign representation. The torsion subgroup is trivial for the alternating groups. The torsion-free part of the group is free abelian of rank 1 if n ≥ p2 + p and has rank 2 if p2 ≤ n < p2 + p. This completes the work begun earlier by Carlson, Mazza and Nakano.

scholarly journals The subnormal subgroup structure of the infinite general linear group

1982 ◽  
Vol 25 (1) ◽  
pp. 81-86 ◽  
Author(s):  
David G. Arrell
Keyword(s):  
General Linear Group ◽  
Subnormal Subgroup ◽  
Complete Classification ◽  
Normal Subgroups ◽  
Finiteness Conditions ◽  
Group Of Units ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Infinite Set

Let R be a ring with identity, let Ω be an infinite set and let M be the free R-module R(Ω). In [1] we investigated the problem of locating and classifying the normal subgroups of GL(Ω, R), the group of units of the endomorphism ring EndRM, where R was an arbitrary ring with identity. (This extended the work of [3] and [8] where it was necessary for R to satisfy certain finiteness conditions.) When R is a division ring, the complete classification of the normal subgroups of GL(Ω, R) is given in [9] and the corresponding results for a Hilbert space are given in [6] and [7]. The object of this paper is to extend the methods of [1] to yield a classification of the subnormal subgroups of GL(Ω, R) along the lines of that given by Wilson in [10] in the finite dimensional case.

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