Answer by Tom Church for Size of the smallest group not satisfying an identity.
The asymptotic version of this question raised by Bjorn Poonen has been studied by Khalid Bou-Rabee for general groups, not just free groups. That is, given G a residually finite group, for each g we...
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To make the question a little less open-ended while (I hope) retaining its spirit, let me interpret the question as asking for the rate of growth of the function $\mu(k)$ defined as the maximum of...
View ArticleSize of the smallest group not satisfying an identity.
Given $F = F(x_0,\ldots,x_n)$ the free group on $n+1$ generators. Define a function $M: F\rightarrow \mathbb{N}$ such that $F(w) = l$, if the smallest group in which $w$ is not an identity is of size...
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