# Tagged Questions

27 views

179 views

### Finding the order of the automorphism group of the abelian group of order 8.

So I am given an abelian group of order $8$ such that for all non-identity elements $x^2 = e$ (all elements have order two). So I know the answer is gonna be $168$, but I gotta prove this. So far I ...
154 views

### Linear algebra of finite abelian groups

Let $\phi:G \to H$ be a surjective homomorphism of finite abelian groups, and let $g_1, \ldots, g_n$ be an irredundant set of generators (from now on, a basis) for $G$. be a basis for $G$, meaning a ...
138 views

### Dimension of subspace fixed by subgroup representation.

If $G$ is an abelian group with cyclic subgroup $H$ and $(\rho,V)$ is a (permutation) representation of $G$. Then I can form a representation of $H$ by considering the composition ...
96 views

### number of differents vector space structures over the same field $\mathbb{F}$ on an abelian group

My question here raised another one. How many differents vector space structures over a field $\mathbb{F}$ we may have on an abelian group? I know that there are abelian groups that we can not endow ...
### Is $\mathbb{Z}(p^{\infty})$ a vector space over some field $\mathbb{F}$?
I don't know how to write in good English, so I will follow Hungerford's word from his book Algebra. The following relation on the additive group $\mathbb{Q}$ of rational numbers is a congruence ...
Ciao! Let $A$ be a finite abelian group, and let $\psi : A \times A \to \mathbb{Q}/\mathbb{Z}$ be an alternating, non-degenerate bilinear form on $A$. Maybe I should say what I mean by these ...