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Abstract
This paper continues a programme of searching for a finite set of generators of a subgroup of finite index in the unit group of an integral group ring of a finite group.
Let $G$ be a finite group. For an antiautomorphism $\varphi$ of $G$, which is naturally extended to $\Bbb Z [G]$, put $$ \scr U _{\varphi}(\Bbb Z [G])= \{u \in \scr U (\Bbb Z [G]) u \,\varphi (u)=1 \}. $$ This group is called the group of $\varphi$unitary units. Let $\varphi _1, \dots , \varphi _n$ be antiautomorphisms of $G$. The author defines $$ \scr U_{ \varphi_{1},\dots , \varphi _{n}}(\Bbb Z [G])= \langle\scr U _{\varphi _{i}}(\Bbb Z[G]) i=1, \dots , n \rangle. $$
The main result of this paper is that if $G$ is a nonabelian group of order less than or equal to $16$, then the Bass cyclic units, the bicyclic units and $\scr U_{ \varphi_{1}, \varphi _{2}}(\Bbb Z [G])$, where $\varphi _1, \varphi _2$ are suitably chosen antiautomorphisms of $G$, generate a subgroup of finite index in $\scr U (\Bbb Z [G])$.
Let $G$ be a finite group. For an antiautomorphism $\varphi$ of $G$, which is naturally extended to $\Bbb Z [G]$, put $$ \scr U _{\varphi}(\Bbb Z [G])= \{u \in \scr U (\Bbb Z [G]) u \,\varphi (u)=1 \}. $$ This group is called the group of $\varphi$unitary units. Let $\varphi _1, \dots , \varphi _n$ be antiautomorphisms of $G$. The author defines $$ \scr U_{ \varphi_{1},\dots , \varphi _{n}}(\Bbb Z [G])= \langle\scr U _{\varphi _{i}}(\Bbb Z[G]) i=1, \dots , n \rangle. $$
The main result of this paper is that if $G$ is a nonabelian group of order less than or equal to $16$, then the Bass cyclic units, the bicyclic units and $\scr U_{ \varphi_{1}, \varphi _{2}}(\Bbb Z [G])$, where $\varphi _1, \varphi _2$ are suitably chosen antiautomorphisms of $G$, generate a subgroup of finite index in $\scr U (\Bbb Z [G])$.
Original language  English 

Pages (fromto)  4352 
Number of pages  10 
Journal  Journal of Algebra and Its Applications 
Volume  5 
Publication status  Published  1 Feb 2006 
Keywords
 unitary
 units
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Dive into the research topics of 'Unitary Units in Integral Group Rings'. Together they form a unique fingerprint.Activities
 1 Talk or presentation at a conference

NonCommutative Algebra Conference
Ann Dooms (Speaker)
1 Sep 2006 → 6 Sep 2006Activity: Talk or presentation › Talk or presentation at a conference