Classification of Normal Congruence Subgroups of the Modular Group

1965 ◽  
Vol 87 (2) ◽  
pp. 285 ◽  
Author(s):  
Donald L. McQuillan
Keyword(s):  
Modular Group ◽  
Congruence Subgroups ◽  
Normal Congruence

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.

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.

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