scholarly journals Construction of free subgroups in the group of units of modular group algebras

1996 ◽  
Vol 24 (13) ◽  
pp. 4211-4215 ◽  
Author(s):  
Jairo Z. Gonçalves ◽  
Donald S. Passman
Keyword(s):  
Modular Group ◽  
Group Algebras ◽  
Group Of Units ◽  
Free Subgroups

A SURVEY ON FREE SUBGROUPS IN THE GROUP OF UNITS OF GROUP RINGS

2013 ◽  
Vol 12 (06) ◽  
pp. 1350004 ◽  
Author(s):  
JAIRO Z. GONÇALVES ◽  
ÁNGEL DEL RÍO
Keyword(s):  
Finite Groups ◽  
Free Groups ◽  
Group Algebras ◽  
Group Rings ◽  
Integral Group ◽  
Natural Group ◽  
Integral Group Rings ◽  
Group Of Units ◽  
Survey Results ◽  
Free Subgroups

In this survey we revise the methods and results on the existence and construction of free groups of units in group rings, with special emphasis in integral group rings over finite groups and group algebras. We also survey results on constructions of free groups generated by elements which are either symmetric or unitary with respect to some involution and other results on which integral group rings have large subgroups which can be constructed with free subgroups and natural group operations.

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

Free Subgroups in the Unit Groups of Integral Group Rings

1980 ◽  
Vol 32 (6) ◽  
pp. 1342-1352 ◽  
Author(s):  
B. Hartley ◽  
P. F. Pickel
Keyword(s):  
Sufficient Conditions ◽  
Finite Subgroup ◽  
Free Subgroup ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Group Of Units ◽  
Rank 2 ◽  
Necessary And Sufficient ◽  
Free Subgroups

Let G be a group, ZG the group ring of G over the ring Z of integers, and U(ZG) the group of units of ZG. One method of investigating U(ZG) is to choose some property of groups and try to determine the groups G such that U(ZG) enjoys that property. For example Sehgal and Zassenhaus [9] have given necessary and sufficient conditions for U(ZG) to be nilpotent (see also [7]), and the same authors have investigated when U(ZG) is an FC (finite-conjugate) group [10]. For a survey of related questions, see [3]. In this paper we consider when U(ZG) contains a free subgroup of rank 2. We conjecture that if this does not happen, then every finite subgroup of G is normal, from which various other conclusions then follow (see Lemma 4).

Central Idempotents and Units in Rational Group Algebras of Alternating Groups

1998 ◽  
Vol 08 (04) ◽  
pp. 467-477 ◽  
Author(s):  
A. Giambruno ◽  
E. Jespers
Keyword(s):  
Group Algebra ◽  
Finite Index ◽  
Explicit Description ◽  
Alternating Group ◽  
Group Algebras ◽  
Young Tableaux ◽  
Rational Group ◽  
Alternating Groups ◽  
Group Of Units

Let ℚAn be the group algebra of the alternating group over the rationals. By exploiting the theory of Young tableaux, we give an explicit description of the minimal central idempotents of ℚAn. As an application we construct finitely many generators for a subgroup of finite index in the centre of the group of units of ℚAn.

scholarly journals Symmetric units in modular group algebras

1996 ◽  
Vol 24 (3) ◽  
pp. 803-808 ◽  
Author(s):  
Victor Bovdi ◽  
L.G. Kovács ◽  
S.K. Sehgal
Keyword(s):  
Modular Group ◽  
Group Algebras
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