Torsion Units in Group Rings and A Conjecture of H.J. Zassenhaus

1986 ◽  
pp. 179-192
Author(s):  
C. Polcino Milies
Keyword(s):  
Group Rings ◽  
Torsion Units

TRIVIAL TORSION UNITS IN G-ADAPTED GROUP RINGS

2006 ◽  
Vol 05 (06) ◽  
pp. 781-791
Author(s):  
ALLEN HERMAN ◽  
YUANLIN LI
Keyword(s):  
Group Ring ◽  
Torsion Group ◽  
Unit Group ◽  
Group Rings ◽  
Quaternion Group ◽  
Torsion Units ◽  
Equivalent Conditions

Let G be a torsion group and let R be a G-adapted ring. In this note we study the question of when the group ring RG has only trivial torsion units. It turns out that the above question is closely related to the question of when the quaternion group ring RQ8 has only trivial torsion units. We first give a ring-theoretic condition on R which determines exactly when the quaternion group ring has only trivial torsion units. Then several equivalent conditions for RG to have only trivial torsion units are provided. We also investigate the hypercenter of the unit group of a G-adapted group ring RG, and show that when R satisfies the torsion trivial involution condition, this hypercenter is not equal to the center if and only if G is a Q*-group.

scholarly journals On the Torsion Units of Integral Adjacency Algebras of Finite Association Schemes

Algebra ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Allen Herman ◽  
Gurmail Singh
Keyword(s):  
Association Scheme ◽  
Association Schemes ◽  
Group Rings ◽  
The 1960S ◽  
Torsion Units

Torsion units of group rings have been studied extensively since the 1960s. As association schemes are generalization of groups, it is natural to ask about torsion units of association scheme rings. In this paper we establish some results about torsion units of association scheme rings analogous to basic results for torsion units of group rings.

Group rings whose torsion units form a subgroup II

1981 ◽  
Vol 9 (7) ◽  
pp. 699-712 ◽  
Author(s):  
César Polcino Milies
Keyword(s):  
Group Rings ◽  
Subgroup Ii ◽  
Torsion Units

scholarly journals Torsion units in integral group rings of metacyclic groups

1984 ◽  
Vol 19 (1) ◽  
pp. 103-114 ◽  
Author(s):  
César Polcino Milies ◽  
Sudarshan K. Sehgal
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Torsion Units

scholarly journals Torsion Units in Infinite Group Rings

1994 ◽  
Vol 47 (3) ◽  
pp. 284-299 ◽  
Author(s):  
A. Bovdi ◽  
Z. Marciniak ◽  
S.K. Sehgal
Keyword(s):  
Infinite Group ◽  
Group Rings ◽  
Torsion Units

scholarly journals On a conjecture of Zassenhaus on torsion units in integral group rings. II

1986 ◽  
Vol 97 (2) ◽  
pp. 201-201 ◽  
Author(s):  
C{ésar Polcino Milies ◽  
J{ürgen Ritter ◽  
Sudarshan K. Sehgal
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Torsion Units
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