The isomorphism problem of unitary subgroups of modular group algebras

2020 ◽  
Vol 97 (1-2) ◽  
pp. 27-39 ◽  
Author(s):  
Zsolt Balogh ◽  
Victor Bovdi





2013 ◽  
Vol 59 (2) ◽  
pp. 415-430
Author(s):  
P.V. Danchev

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.



Author(s):  
Diego García-Lucas ◽  
Leo Margolis ◽  
Ángel del Río

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.



1988 ◽  
Vol 40 (6) ◽  
pp. 1422-1435 ◽  
Author(s):  
C. Bagiński ◽  
A. Caranti

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.



1976 ◽  
Vol 41 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Jon F Carlson


1997 ◽  
Vol 25 (12) ◽  
pp. 3751-3760 ◽  
Author(s):  
William Ullery


1990 ◽  
Vol 42 (3) ◽  
pp. 383-394 ◽  
Author(s):  
Frank Röhl

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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