3
votes
1answer
55 views

Calculating a cokernel on wedge product

i have a question... maybe it is easy and im only doing some mistake. Given a surjective homomorphism $f\colon \mathbb{Z}^n \rightarrow \mathbb{Z}^m$, then its kernel $K_f$ is isomorphic to ...
1
vote
1answer
136 views

Direct sum and tensor product of two representations of a group

Our lecturer gave us a hard exercice to go further in group theory (we stopped at group actions) : Let G be a group, V and W complex vector spaces and $\rho_1 : G \mapsto GL(V) $ be a group ...
15
votes
2answers
225 views

Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative

$\def\sign{\operatorname{sign}}$ For homework, I am trying to show that $\sign:S_n \to \{\pm 1\}$ is multiplicative, i.e. that for any permutations $\sigma_1,\sigma_2$ we have $$\sign(\sigma_1 ...