# Tagged Questions

44 views

### Basic proof of statement in abstract algebra?

http://www.proofwiki.org/wiki/Abelian_Quotient_Group The third step (in both proofs) is something I am having trouble seeing. The theorem itself is not difficult to prove, but it is much cleaner this ...
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### subgroup proof.

Prove that if $G$ is an abelian group, then $H =\{ x \in G\mid x^{2} = e \}$ is a subgroup of $G$. I did show that $H$ is close, associative, have identity and inverse element. Then my prof said I ...
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### “Classify $\mathbb{Z}_5 \times \mathbb{Z}_4 \times \mathbb{Z}_8 / \langle(1,1,1)\rangle$”

I have a question that says this: Classify $\mathbb{Z}_5 \times \mathbb{Z}_4 \times \mathbb{Z}_8 / \langle(1,1,1)\rangle$ according to the fundamental theorem of finitely generated abelian groups. ...
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### Ordered abelian groups

Consider the following axioms: 1) $\ x+(y+z)=(x+y)+z$ ; $\forall x \forall y \forall z$ 2) $\ x+0=x$ ; $\forall x$ 3) $\forall x$ $\exists y$ such that $\ x+y=0$ 4) $\ x+y=y+x$ ...
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### G is an abelian group. Prove $G^{(n)}$ is a subgroup of G

Let G be an abelian group. Prove that $$G^{(n)} = \{g \in G | g^n = 1_G \}$$ is a subgroup of G. How do I go about doing this? I understand that $G^{(n)}$ is basically the set of all elements ...
### Prove $H \times G$ is commutative iff $H, G$ are commutative
This is another proof question I am asking about, can someone give me tips on how to answer these questions? My question says: "Let $H,G$ be arbitrary groups. Prove that $H \times G$ is commutative ...
### Computing Quotient Groups $\mathbb{Z}_4 \times \mathbb{Z}_{10} / \langle (2, 4) \rangle$, $\mathbb{Z} \times \mathbb{Z}_{6}/ \langle (1, 2) \rangle$
Let $G/H = \mathbb{Z}_{4} \times \mathbb{Z}_{10} / \langle (2, 4) \rangle$. I know that $|G/H|$ = 4, so $G/H \simeq \mathbb{Z}_{2} \times \mathbb{Z}_{2}$ or $\mathbb{Z}_{4}$. Since $G/H$ has an ...