On Non-Congruence Subgroups of the Analogue of the Modular Group in Characteristic p

2003 ◽  
pp. 141-144
Author(s):  
A. W. Mason
Keyword(s):  
Modular Group ◽  
Congruence Subgroups ◽  
Characteristic P

ON THE CENTER OF THE MODULAR GROUP ALGEBRA OF A FINITE p-GROUP

2014 ◽  
Vol 13 (04) ◽  
pp. 1350127
Author(s):  
CZESŁAW BAGIŃSKI ◽  
JÁNOS KURDICS
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Conjugacy Classes ◽  
Characteristic P ◽  
Cyclic Groups ◽  
Modular Group Algebra ◽  
Index 2 ◽  
Zero Multiplication

Let G be a finite nonabelian p-group and F a field of characteristic p and let [Formula: see text] be the subalgebra spanned by class sums [Formula: see text], where C runs over all conjugacy classes of noncentral elements of G. We show that all finite p-groups are subgroups and homomorphic images of p-groups for which [Formula: see text]. We also give the description of abelian-by-cyclic groups for which [Formula: see text] is an algebra with zero multiplication or is nil of index 2.

scholarly journals Macbeath's curve and the modular group

1985 ◽  
Vol 27 ◽  
pp. 239-247 ◽  
Author(s):  
K. Wohlfahrt
Keyword(s):  
Finite Index ◽  
Modular Group ◽  
Algebraic Curves ◽  
The Other ◽  
Congruence Subgroups ◽  
Related Research ◽  
Other Hand

The theory of algebraic curves associated with subgroups of finite index in the modular group Γ is highly developed for such subgroups of Γ as may be defined by means of congruences in the ring ℤ of rational integers. The situation in he case of non-congruence subgroups of Γ, on the other hand, is drastically different. It reduces to a few isolated examples, two of which may be found in [12]. Related research by A. O. L. Atkin and H. P. F. Swinnerton-Dyer began in [1].

scholarly journals Lie Nilpotency Indices of Modular Group Algebras

2010 ◽  
Vol 17 (01) ◽  
pp. 17-26 ◽  
Author(s):  
V. Bovdi ◽  
J. B. Srivastava
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Commutator Subgroup ◽  
Positive Characteristic ◽  
Group Algebras ◽  
Characteristic P ◽  
Nilpotency Index ◽  
Field Of Positive Characteristic

Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that if KG is Lie nilpotent, then its upper (or lower) Lie nilpotency index is at most |G′| + 1, where |G′| is the order of the commutator subgroup. The class of groups G for which these indices are maximal or almost maximal has already been determined. Here we determine G for which upper (or lower) Lie nilpotency index is the next highest possible.

Sign in / Sign up

Export Citation Format

Share Document