scholarly journals Non-isomorphic 2-groups with isomorphic modular group algebras

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Diego García-Lucas ◽  
Leo Margolis ◽  
Ángel del Río
Keyword(s):  
Modular Group ◽  
Isomorphism Problem ◽  
Group Algebras ◽  
Isomorphic Group ◽  
Characteristic 2

Abstract We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

Commutative Modular Group Algebras of Special Classes of Abelian Groups

2013 ◽  
Vol 59 (2) ◽  
pp. 415-430
Author(s):  
P.V. Danchev
Keyword(s):  
Modular Group ◽  
Abelian Groups ◽  
Classification Problem ◽  
Isomorphism Problem ◽  
Group Algebras ◽  
Direct Factor ◽  
Factor Problem ◽  
Special Classes

Abstract Structural results on the Direct Factor Problem, the Classification Problem and the Isomorphism Problem are proved for modular group algebras of certain sorts of abelian groups.

A note on normal complement problem

2017 ◽  
Vol 16 (01) ◽  
pp. 1750011 ◽  
Author(s):  
K. Kaur ◽  
M. Khan ◽  
T. Chatterjee
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Positive Characteristic ◽  
Unit Group ◽  
Semisimple Group ◽  
Group Algebras ◽  
Metacyclic Group ◽  
Infinite Class ◽  
Normal Complement ◽  
Characteristic 2

In this paper, we study the normal complement problem on semisimple group algebras and modular group algebras [Formula: see text] over a field [Formula: see text] of positive characteristic. We provide an infinite class of abelian groups [Formula: see text] and Galois fields [Formula: see text] that have normal complement in the unit group [Formula: see text] for semisimple group algebras [Formula: see text]. For metacyclic group [Formula: see text] of order [Formula: see text], where [Formula: see text] are distinct primes, we prove that [Formula: see text] does not have normal complement in [Formula: see text] for finite semisimple group algebra [Formula: see text]. Finally, we study the normal complement problem for modular group algebras over field of characteristic 2.

The Modular Group Algebras of P-Groups of Maximal Class

1988 ◽  
Vol 40 (6) ◽  
pp. 1422-1435 ◽  
Author(s):  
C. Bagiński ◽  
A. Caranti
Keyword(s):  
Maximal Subgroup ◽  
Modular Group ◽  
Isomorphism Problem ◽  
Group Algebras ◽  
Maximal Class ◽  
Special Classes

The isomorphism problem for modular group algebras of finite p-groups appears to be still far from a solution (see [7] for a survey of the existing results). It is therefore of interest to investigate the problem for special classes of groups.The groups we consider here are the p-groups of maximal class, which were extensively studied by Blackburn [1]. In this paper we solve the modular isomorphism problem for such groups of order not larger than pp+1, having an abelian maximal subgroup, for odd primes p.What we in fact do is to generalize methods used by Passman [5] to solve the isomorphism problem for groups of order p4. In Passman's paper the case of groups of maximal class is actually the most difficult one.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals Almost free modules over modular group algebras

1976 ◽  
Vol 41 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Jon F Carlson
Keyword(s):  
Modular Group ◽  
Group Algebras ◽  
Free Modules
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