The isomorphism problem of unitary subgroups of modular group algebras

2020 ◽  
Vol 97 (1-2) ◽  
pp. 27-39 ◽  
Author(s):  
Zsolt Balogh ◽  
Victor Bovdi
Keyword(s):  
Modular Group ◽  
Isomorphism Problem ◽  
Group Algebras

scholarly journals On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups

1999 ◽  
Vol 82 (1) ◽  
pp. 125-136
Author(s):  
Czesław Bagiński
Keyword(s):  
Modular Group ◽  
Isomorphism Problem ◽  
Group Algebras

Unit Groups of Completed Modular Group Algebras and the Isomorphism Problem

1991 ◽  
Vol 111 (3) ◽  
pp. 611
Author(s):  
Frank Rohl
Keyword(s):  
Modular Group ◽  
Isomorphism Problem ◽  
Group Algebras

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.

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.

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 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

Units of modular group algebras of abelian groups of cardinality N2

1997 ◽  
Vol 25 (12) ◽  
pp. 3751-3760 ◽  
Author(s):  
William Ullery
Keyword(s):  
Modular Group ◽  
Abelian Groups ◽  
Group Algebras

On Automorphisms of Complete Algebras And The Isomorphism Problem for Modular Group Rings

1990 ◽  
Vol 42 (3) ◽  
pp. 383-394 ◽  
Author(s):  
Frank Röhl
Keyword(s):  
Group Ring ◽  
Modular Group ◽  
Isomorphism Problem ◽  
Nilpotency Class ◽  
Affirmative Answer ◽  
Integral Group Ring ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Analogous Question

In [5], Roggenkamp and Scott gave an affirmative answer to the isomorphism problem for integral group rings of finite p-groups G and H, i.e. to the question whether ZG ⥲ ZH implies G ⥲ H (in this case, G is said to be characterized by its integral group ring). Progress on the analogous question with Z replaced by the field Fp of p elements has been very little during the last couple of years; and the most far reaching result in this area in a certain sense - due to Passi and Sehgal, see [8] - may be compared to the integral case, where the group G is of nilpotency class 2.

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