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A description of the derived subgroup of a semidirect product, from which the abelianization can be obtained, was published in: Daciberg Lima Gonçalves, John Guaschi The lower central and derived ser …

In an informal talk I heard a statement: "Any cyclic subgroup in a linear group is at most exponentially distorted" with a vague reference to a work of Lubotzky with coauthors. The works of Lubotzk …

Actually there is a simple reasoning showing residual finiteness of free groups using coverings. Indeed, consider the free group $F(n)$ as a fundamental group of a wedge $X$ of $n$ circles. Take any n …

I am looking for an explicit representation of the fundamental group of a closed orientable surface of genus >1. I guess they should be abundant in degree 2. Did anyone see the explicit matrix constru …

Let $X=\{x_1,\dots,x_N\}$ and $F=F(X)$ be a free group generated by $X$. Let $\phi\colon F\to F$ be an automorphism of $F$. Define a growth function of $\phi$ as: $$ \operatorname{gr}_{\phi,X}(n)=\ope …

Fractional derivatives has been defined and found useful in some contexts.

Burnside proved in [1] that the order of $B(2,4)$ is $\le4096$. Tobin proved in [4] that this number is the correct order for this group. A short presentation for $B(2,4)$ was given by Leech in [3], w …