0

Let $G$ be a multiplicative group, and let $\prod_{i=1}^ng_i^{e_i}=1$, $\prod_{i=1}^mh_i^{f_i}=1$ be two multiplicative relations in $G$. What does it mean that these two relation are independent?

Or Shahar
  • 1,766
  • 1
    Relations are dependent if one can be deduced from the others. If $g_1^2=e=g_2^3$ then $g_1^2g_2^3=e$ would be a dependent relation. Of course, it's a more subtle dependence than, say, that of linear dependence in a vector space. Knowing that relation $A$ implies relation $B$ does not tell you that $B$ implies $A$. In a free group, it can be profoundly difficult (even undecidable) to determine whether a collection of relations is dependent. – lulu Jan 13 '23 at 12:15
  • Now I understand... Thank you! – Or Shahar Jan 13 '23 at 13:10

0 Answers0