Sobre grupos com condições polinomiais cúbicas
Salvato in:
| Autore principale: | |
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| Data di pubblicazione: | 2017 |
| Natura: | Master thesis |
| Lingua: | por |
| Fonte: | Repositório Institucional da UFG |
| Download full: | http://repositorio.bc.ufg.br/tede/handle/tede/7792 |
Riassunto: | Let $F_d$ be the free group of rank $d$, freely generated by $\{y_1,...,y_d\}$, $\mathbb{D}F_d$ the group ring over an integral domain $\mathbb{D}$, $E_d$ subset of $F_d$ containing $\{y_1,...,y_d\}$, $p_s(x)=x^n+c_{s,n-1}x^{n-1}+...+c_{s,1}x+c_{s,0} \in \mathbb{D}[x]$ a monic polynomial and the quotient ring $$A(d,n,E_d)=\frac{\mathbb{D}F_d}{\langle p_s(s):s\in E_d \rangle_{ideal}}.$$ When $p_s(s)$ is cubic for all $s$, we construct a finite set $E_d$ such that $A(d,n,E_d)$ has finite rank over an extension of $\mathbb{D}$. In the case where all polynomials are equal to $(x-1)^3$ and $\mathbb{D}=\mathbb{Z}[\frac{1}{6}]$ we construct a finite subset $P_d$ of $F_d$ such that $A(d,3,P_d)$ has finite $\mathbb{D}$-rank and its augmentation ideal is nilponte. Furthermore $(x-1)^3$is satisfied by all elements in the image of $F_2$ in $A(2,3,P_2)$. |