Newbetuts
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New posts in abelian-groups
In a group we have $abc=cba$. Is it abelian?
group-theory
abelian-groups
Abelian group order divides lcm
abstract-algebra
group-theory
abelian-groups
Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
group-theory
abelian-groups
Showing that a finite abelian group has a subgroup of order $m$ for each divisor $m$ of $n$
abstract-algebra
group-theory
finite-groups
abelian-groups
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
abstract-algebra
group-theory
finite-groups
abelian-groups
Structure Theorem for abelian torsion groups that are not finitely generated?
abstract-algebra
group-theory
modules
abelian-groups
Group of positive rationals under multiplication not isomorphic to group of rationals
group-theory
abelian-groups
group-isomorphism
A nonsplit short exact sequence of abelian groups with $B \cong A \oplus C$
abstract-algebra
abelian-groups
exact-sequence
Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
group-theory
abelian-groups
group-isomorphism
A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian?
abstract-algebra
group-theory
abelian-groups
Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
abstract-algebra
group-theory
abelian-groups
Let $G$ be a abelian group such that $|G| = 2p$ and $p$ Is a odd prime number. Prove $G$ is a cyclic group. [duplicate]
group-theory
abelian-groups
cyclic-groups
Product of elements of a finite abelian group
abstract-algebra
group-theory
finite-groups
abelian-groups
Finding an explicit isomorphism from $\mathbb{Z}^{4}/H$ to $\mathbb{Z} \oplus \mathbb{Z}/18\mathbb{Z}$
abstract-algebra
modules
abelian-groups
Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
group-theory
abelian-groups
finitely-generated
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
group-theory
abelian-groups
How to recognize a finitely generated abelian group as a product of cyclic groups.
abstract-algebra
group-theory
abelian-groups
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
group-theory
abelian-groups
Group of order 15 is abelian
abstract-algebra
group-theory
finite-groups
abelian-groups
The direct sum $\oplus$ versus the cartesian product $\times$
group-theory
abelian-groups
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