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New posts in quotient-group
If $H$ is a subgroup of a finite abelian group $G$, then $G$ has a subgroup that is isomorphic to $G/H$.
group-theory
abelian-groups
group-isomorphism
quotient-group
direct-product
Conditions for cyclic quotient group
group-theory
finite-groups
cyclic-groups
quotient-group
Let $H\leq G$. Prove $x^{-1}y^{-1}xy\in H\text{ }\forall x,y\in G \iff H\trianglelefteq G \text{ and } G/H \text{ is abelian}$.
abstract-algebra
group-theory
abelian-groups
normal-subgroups
quotient-group
Is it true that for a Group $G$ with Normal Group $N: G/N = GN/N$?
abstract-algebra
group-theory
normal-subgroups
quotient-group
Is $\Bbb R/\Bbb Z$ isomorphic to $\Bbb R/2\Bbb Z$?
group-isomorphism
quotient-group
Between the center of a quotient group and the total center
abstract-algebra
group-theory
normal-subgroups
quotient-group
If $G$ is cyclic then $G/H$ is cyclic?
abstract-algebra
group-theory
cyclic-groups
quotient-group
Cyclicness of a quotient of subgroups of infinite cyclic group
abstract-algebra
group-theory
symmetric-groups
cyclic-groups
quotient-group
Let $H$ be the subgroup of $\Bbb Z^3$ generated by elements $(5,−4, 3), (7, 2, 3)$ and $(21, 8, 9)$. Classify the factor group $\Bbb Z^{3}/H$.
abstract-algebra
group-theory
quotient-group
Discuss $\mathbb R[X]/(aX^2 +bX + c)$ in terms of $\Delta = b^2-4ac$
abstract-algebra
polynomials
ring-theory
irreducible-polynomials
quotient-group
Give an example of: A group with an element A of order 3, an element B with order 4, where order of AB is less than 12
group-theory
quotient-group
Why is the fact that a quotient group is a group relevant?
abstract-algebra
group-theory
soft-question
motivation
quotient-group
Justify $\frac{\mathbb{Z}_a\times \mathbb{Z}_b}{\langle a/c\rangle \times \langle b/d\rangle}$ is isomorphic to $\mathbb{Z}_c\times \mathbb{Z}_d$.
group-theory
abelian-groups
group-isomorphism
quotient-group
When is $G/N \cong H/K$?
abstract-algebra
group-theory
normal-subgroups
group-isomorphism
quotient-group
Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$
abstract-algebra
integers
group-isomorphism
quotient-group
Understanding a proof of: If $N\unlhd G$ s.t. $N$ and $G/N$ are solvable, then $G$ is solvable.
group-theory
proof-explanation
normal-subgroups
quotient-group
solvable-groups
Number of subgroup $G<\Bbb Z^3$ such that $\Bbb Z^3/G\simeq \Bbb Z/3\Bbb Z\oplus\Bbb Z/3\Bbb Z$ [closed]
abstract-algebra
group-theory
modules
quotient-group
Finding quotient of additive abelian group in Sage
group-theory
finite-groups
abelian-groups
quotient-group
sagemath
Why the term and the concept of quotient group?
abstract-algebra
group-theory
quotient-group
Why do we define quotient groups for normal subgroups only?
group-theory
normal-subgroups
quotient-group
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