Newbetuts

Difficulty showing that a group $G$ applied on $X$, $G_x$ ($x \in X$) & $G_y$, w/ $y \in G(x)$ are same iff $G_x$ is a normal subgroup of $G$. [duplicate]

Do subgroup and quotient group define a group?

For an action of $G$ on a set, every point of some orbit has the same stabilizer if and only if this stabilizer is a normal subgroup.

Let $H$ be a subgroup of group $G$ and $K$ be a normal subgroup of $G$ such that $\gcd([G:H], |K|) = 1$. Prove that $K \subseteq H$ [closed]

Prove that in a nilpotent group every normal subgroup of prime order is contained in the center.

Subgroup of the free group on 3 generators

Prove that the cyclic subgroup $\langle a\rangle$ of a group $G$ is normal if and only if for each $g\in G$, $ga=a^kg$ for some $k\in\Bbb{Z}$.

$K \lhd G, \space \space G/K \simeq H_1$, and $K \simeq H_2$

$S_4/V_4$ isomorphic to $S_3$ - Understanding Attached Tables

Product of cosets of normal subgroup and well-definedness

If a nilpotent group has an element of prime order $p$, so does its centre.

Let $H\leq G$. Prove $x^{-1}y^{-1}xy\in H\text{ }\forall x,y\in G \iff H\trianglelefteq G \text{ and } G/H \text{ is abelian}$.

Prove that if $G\leq S_n$ of index $2$, then $G=A_n$. [duplicate]

Every subgroup of a quotient group is a quotient group itself

New posts in normal-subgroups

What are the self-normalizing subgroups of $S_n$?

Normal subgroup: a problem in Verification of equivalence

Normalizer and centralizer are equivalent when $p$ is the smallest prime dividing $|G|$

Assume $H,G$ are simple groups. Can we prove that either $H\unlhd HG$ or $H\unlhd GH$?

If Cylic subgroup implies abelian implies normal then how A5 is simple group [closed]

Prove every group of order less or equal to five is abelian [closed]

Difficulty showing that a group $G$ applied on $X$, $G_x$ ($x \in X$) & $G_y$, w/ $y \in G(x)$ are same iff $G_x$ is a normal subgroup of $G$. [duplicate]

Do subgroup and quotient group define a group?

For an action of $G$ on a set, every point of some orbit has the same stabilizer if and only if this stabilizer is a normal subgroup.

Let $H$ be a subgroup of group $G$ and $K$ be a normal subgroup of $G$ such that $\gcd([G:H], |K|) = 1$. Prove that $K \subseteq H$ [closed]

Prove that in a nilpotent group every normal subgroup of prime order is contained in the center.

Subgroup of the free group on 3 generators

Prove that the cyclic subgroup $\langle a\rangle$ of a group $G$ is normal if and only if for each $g\in G$, $ga=a^kg$ for some $k\in\Bbb{Z}$.

$K \lhd G, \space \space G/K \simeq H_1$, and $K \simeq H_2$

$S_4/V_4$ isomorphic to $S_3$ - Understanding Attached Tables

Product of cosets of normal subgroup and well-definedness

If a nilpotent group has an element of prime order $p$, so does its centre.

Let $H\leq G$. Prove $x^{-1}y^{-1}xy\in H\text{ }\forall x,y\in G \iff H\trianglelefteq G \text{ and } G/H \text{ is abelian}$.

Prove that if $G\leq S_n$ of index $2$, then $G=A_n$. [duplicate]

Every subgroup of a quotient group is a quotient group itself