The outer-automorphisms tag has no usage guidance.

**4**

votes

**1**answer

108 views

### Genericity of irreducible automorphisms of free groups

I have seen in the literature that Irreducible outer automorphisms of a free group $F_n$ are "generic".
I would like to ask that if for example : it is true that for any generating set $X$ of $Out(...

**6**

votes

**0**answers

132 views

### Outer automorphisms of direct product of residually finite groups

Let $A,B$ be finite generated residually finite groups such that $\mathop{Out}(A)$ and $\mathop{Out}(B)$ are residually finite.
Is $\mathop{Out}(A\times B)$ residually finite?
If not, what is the ...

**3**

votes

**0**answers

146 views

### On a problem of Berkovich

What is the real history of the following problem proposed by Berkovich [Y. Berkovich, Z.Janko, Groups of prime power order. Volume 2, Expositions in Mathematics, 56, Walter de Gruyter, New York, 2011]...

**10**

votes

**2**answers

545 views

### Centralizers of non-iwip elements of $Out(F_n)$

Does there exist an infinite order element $\phi\in Out(F_n)$, for some or all $n\geq 3$, which is not iwip but has finite index in its centralizer? How about an element such that all its non-zero ...

**9**

votes

**2**answers

488 views

### Outer automorphisms of free groups into bigger free groups

This may be very either very simple or very unknown, but here goes: Let $F_n$ be the free group on $n$ generators and $Out(F_n)$ its outer automorphism group.
Can embeddings $Out(F_n) \...

**5**

votes

**1**answer

394 views

### What is Out(G-mod) for a finite group G?

Following the notation of Etingof-Nikshych-Ostrik what is Out(G-mod) for a finite group G?
That is what are all bimodule cateogries over the fusion category G-mod of complex G-modules which have the ...