5,672 research outputs found
Wreath products in modular group algebras of some finite 2-groups
Let be field of characteristic 2 and let be a finite non-abelian
2-group with the cyclic derived subgroup , and there exists a central
element of order 2 in . We prove that the unit group of
the group algebra possesses a section isomorphic to the wreath product of
a group of order 2 with the derived subgroup of the group , giving for such
groups a positive answer to the question of A. Shalev.Comment: 3 page
Rewriting the check of 8-rewritability for
The group is called -rewritable for , if for each sequence of
elements there exists a non-identity permutation
such that . Using computers, Blyth and Robinson (1990) verified that
the alternating group is 8-rewritable. We report on an independent
verification of this statement using the computational algebra system GAP, and
compare the performance of our sequential and parallel code with the original
one.Comment: 5 page
Wreath Products in the Unit Group of Modular Group Algebras of 2-groups of Maximal Class
We study the unit group of the modular group algebra KG, where G is a 2-group
of maximal class. We prove that the unit group of KG possesses a section
isomorphic to the wreath product of a group of order two with the commutator
subgroup of the group G.Comment: 12 pages, LaTe
On the isomorphism problem for unit groups of modular group algebras
Using the computational algebra system GAP (http://www.gap-system.org) and
the GAP package LAGUNA (http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm), we
checked that all 2-groups of order not greater than 32 are determined by
normalized unit groups of their modular group algebras over the field of two
elements.Comment: 6 pages, accepted in Acta Sci. Math. (Szeged
The modular isomorphism problem for finite -groups with a cyclic subgroup of index
Let be a prime number, be a finite -group and be a field of
characteristic . The Modular Isomorphism Problem (MIP) asks whether the
group algebra determines the group . Dealing with MIP, we investigated
a question whether the nilpotency class of a finite -group is determined by
its modular group algebra over the field of elements. We give a positive
answer to this question provided one of the following conditions holds: (i)
; (ii) \cl(G)=2; (iii) is cyclic; (iv) is a group of
maximal class and contains an abelian subgroup of index .Comment: 8 page
On 2-groups of almost maximal class
Let G be a 2-group of order 2^n, n>5, and nilpotency class n-2. The
invariants of such groups determined by their group algebras over the field of
two elements are given in the paper.Comment: 25 page
Integral group ring of the first Mathieu simple group
We investigate the classical Zassenhaus conjecture for the normalized unit group
of the integral group ring of the simple Mathieu group M11. As a consequence, for
this group we confirm the conjecture by Kimmerle about prime graphs
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