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New posts in normal-subgroups
How to show that Klein four-group is a normal subgroup of the alternating group $A_4$
group-theory
normal-subgroups
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
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$ [duplicate]
group-theory
normal-subgroups
Some Subgroup of Dihedral Group is Normal
abstract-algebra
group-theory
normal-subgroups
dihedral-groups
Intersection of conjugate subgroups is normal
abstract-algebra
group-theory
normal-subgroups
Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$
abstract-algebra
group-theory
normal-subgroups
Are there any natural numbers $n$ that satisfy the condition $7921\sigma(n) = 15840n$?
group-theory
elementary-number-theory
finite-groups
normal-subgroups
divisor-sum
Prove that the center of a group is a normal subgroup [closed]
abstract-algebra
group-theory
normal-subgroups
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
abstract-algebra
group-theory
normal-subgroups
If $N$ is a normal subgroup of $G$, show $Z(G)N/N \subset Z(G/N)$ [closed]
abstract-algebra
group-theory
normal-subgroups
nilpotent-groups
All $p$-groups have a normal subgroup of each possible order. [duplicate]
abstract-algebra
group-theory
normal-subgroups
p-groups
Prove that: A group $G$ of order $p^n$ has normal subgroup of order $p^k$, for all $0\le k\le n$.
abstract-algebra
group-theory
normal-subgroups
p-groups
If $N$ is normal in $G$, show $Z_{i}(G)N/N \leq Z_{i}(G/N)$ where $Z_{i}(G)$ is the $i$th term in the upper central series for $G$.
abstract-algebra
group-theory
normal-subgroups
nilpotent-groups
If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.
abstract-algebra
group-theory
cyclic-groups
normal-subgroups
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
abstract-algebra
group-theory
normal-subgroups
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
group-theory
finite-groups
sylow-theory
normal-subgroups
Intuition behind normal subgroups
group-theory
intuition
normal-subgroups
Are normal subgroups transitive?
group-theory
examples-counterexamples
normal-subgroups
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
abstract-algebra
group-theory
normal-subgroups
Normal subgroups of $S_4$
abstract-algebra
group-theory
symmetric-groups
normal-subgroups
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