# Questions tagged [automorphism-groups]

Questions about the group of automorphisms of any mathematical object $X$ endowed with a given structure, i.e the group of all bijective maps from $X$ to itself preserving this structure, and hence helping study it further and understand it better.

**8**

**2**answers

### Is the automorphism group of free group of rank two relatively hyperbolic?

**1**

**0**answers

### Aut/Inn/Out Automorphism Groups of the unitary group $𝑈(𝑁)$

**3**

**1**answer

### On cospectral graphs

**5**

**0**answers

### Copies of the reals in $\mathbb{C}$ without the Axiom of Choice

**13**

**1**answer

### Why is the automorphism group of the octonions $G_2$ instead of $SO(7)$

**7**

**1**answer

### Howson property of automorphism group of $F_2$ and of $F_3$

**1**

**1**answer

### Automorphisms of the ring of Laurent polynomials

**2**

**1**answer

### Automorphisms of $G/Z(G)$ with $G$ simply connected

**8**

**2**answers

### On $p$-groups with abelian automorphism group

**1**

**1**answer

### When is a infinite transcendence-degree rigid fields fixed by a finite extension?

**4**

**2**answers

### Can every involution of a symmetric directed graph be written as a power of another symmetry?

**1**

**0**answers

### Is it always possible to improve the derivation by exponential conjugations?

**7**

**1**answer

### Automorphisms over finite field that do not lift to an automorphism in characteristic zero

**1**

**1**answer

### An automorphism of a function field

**5**

**1**answer

### What are the “simplest” polytopes with an automorphism group of $\mathrm M_{11} \hspace {-1.25pt} $?

**6**

**1**answer

### Does Aut(G) → Out(G) always split for a compact, connected Lie group G?

**5**

**1**answer

### Outer automorphism group of posets

**1**

**0**answers

### similar homomorphisms and conjugate subgroups

**8**

**0**answers

### Automorphism groups of the complex numbers, and other fields

**9**

**1**answer

### What is the automorphism group of the projective line minus $n$ points?

**2**

**0**answers

### Automorphisms group of complex and real simple Lie algebras

**3**

**1**answer

### Spectral properties of half-transitive graphs

**2**

**1**answer

### Explicit automorphism map of ${\rm Spin}(8;\mathbb{R})$, ${\rm SO}(8;\mathbb{R})$, ${\rm PSO}(8;\mathbb{R})$

**10**

**0**answers

### Does the tropicalization of a curve remember the curve's automorphism group?

**1**

**0**answers

### Automorphism groups of Kähler–Einstein manifolds

**1**

**1**answer

### Why $G/F(G)$ is isomorphic to a subgroup of ${\rm Out}(F(G))$?

**1**

**0**answers

### Action on cohomology by automorphisms of ihs manifolds

**2**

**0**answers

### On automorphism group

**9**

**0**answers

### Which finite solvable groups have solvable automorphism groups?

**12**

**1**answer

### On the iterated automorphism groups of the cyclic groups

**2**

**0**answers

### Complexity of computing the automorphism group of the subdivision of clique with leaves

**10**

**1**answer

### Small automorphism groups of groups

**1**

**0**answers

### English translation of Fouxe-Rabinovitch paper

**5**

**1**answer

### Can the automorphism group vary too much in families of complex projective varieties?

**3**

**0**answers

### Automorphism group of a hypersurface and its sections

**1**

**0**answers

### Are there multiple conjugacy classes of order 2 elements in the smooth automorphism group of $\mathbb{R}$?

**12**

**2**answers

### Does asymmetric fraction of finite groups tend to $0$?

**11**

**1**answer

### On certain order-automorphisms of the rationals

**2**

**1**answer

### Fundamental theorem of linear orders

**2**

**0**answers

### What are the compact Aut(A) of an algebra A(G), G finite, that contains the identity?

**0**

**0**answers

### Automorphism group of the cycle graph with $k$ diagonals

**4**

**0**answers

### Are all verbal automorphisms inner power automorphisms?

**3**

**1**answer

### Infinite order automorphisms of planar polynomials

**2**

**1**answer

### Abelian torsion-free group with $\mathbb{Z}_2\times\mathbb{Z}$ as automorphism group

**6**

**1**answer

### Automorphism group of the special unitary group $SU(N)$

**7**

**0**answers

### Automorphism group of poset of number fields

**4**

**1**answer

### Metrics with prescribed Levi-Civita connection

**1**

**1**answer

### Sabidussi theorem for morphisms between graphs

**1**

**1**answer

### What are the holomorphic automorphism groups of unit ball, polydisc, and Hartogs domain in C^n ( n>1)? [closed]

**9**

**1**answer