# Tagged Questions

**1**

vote

**1**answer

106 views

### Amenable normal closure

Prove or disprove:
Let $G$ be a countable group. Let $H < G$ be an amenable subgroup with a finite conjugacy class. Then the normal closure of $H$ is also amenable.
Thanks!

**3**

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**0**answers

87 views

### Cogrowth and value of its series at the critical exponent

Let $G$ be a finitely generated group and write $G = F/N$ for $N$ a normal subgroup of a free group $F$. Let $S_n$ be the elements in $F$ written as words of exactly $n$ letters. So, for $n\geq 1$, ...

**5**

votes

**1**answer

194 views

### Cocycles for right- and left- regular representations on $\ell_2(G)$

Using the standard notation, let $\lambda_gf(x)=f(g^{-1}x)$ be the left regular representation and $\rho_gf(x)=f(xg)$ be the right regular one, acting on the space $V$ of complex-values functions on ...