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.

On the order of unitary subgroup of the modular group algebra 𝔽2kD2N

2015 ◽  
Vol 14 (08) ◽  
pp. 1550129 ◽  
Author(s):  
Neha Makhijani ◽  
R. K. Sharma ◽  
J. B. Srivastava
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Dihedral Group ◽  
Group Of Units ◽  
Modular Group Algebra ◽  
Canonical Involution ◽  
Unitary Subgroup

Let 𝔽qD2N be the group algebra of D2N, the dihedral group of order 2N, over 𝔽q = GF (q). In this paper, we compute the order of the unitary subgroup of the group of units of 𝔽2kD2N with respect to the canonical involution ∗.

Units in modular group algebra

2016 ◽  
Vol 45 (3) ◽  
pp. 971-976 ◽  
Author(s):  
Kuldeep Kaur ◽  
Manju Khan
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Modular Group Algebra

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.

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