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New posts in normal-subgroups
Is it true that for a Group $G$ with Normal Group $N: G/N = GN/N$?
abstract-algebra
group-theory
normal-subgroups
quotient-group
If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$
group-theory
abelian-groups
normal-subgroups
Are all normal subgroups Abelian?
group-theory
normal-subgroups
Questions on Proofs - Equivalent Conditions of Normal Subgroup - Fraleigh p. 141 Theorem 14.13
group-theory
proof-verification
intuition
normal-subgroups
Let $|G|=735$. If the number of Sylow $7$-subgroups are more than $1$, then show that there exists a normal Sylow $5$-subgroup.
group-theory
finite-groups
normal-subgroups
sylow-theory
Characterization of nilpotency with normal subgroups
group-theory
finite-groups
normal-subgroups
nilpotent-groups
Commutator subgroup and subgroup generated by square.
group-theory
normal-subgroups
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
group-theory
finite-groups
abelian-groups
normal-subgroups
Show that SO(n) is a normal subgroup of O(n)
linear-algebra
abstract-algebra
group-theory
matrices
normal-subgroups
Let $G$ be a group and let $H_1,H_2\unlhd G$ such that $H_1\cap H_2 = \{1\}$ and $H_1H_2=G.$ Prove $G\simeq H_1\times H_2$ [duplicate]
group-theory
normal-subgroups
direct-product
Group containing no subgroup of index 2 [closed]
group-theory
normal-subgroups
Between the center of a quotient group and the total center
abstract-algebra
group-theory
normal-subgroups
quotient-group
Why are there 5 subgroups that are generated by double transpositions on four elements in $S_5$?
abstract-algebra
combinatorics
group-theory
symmetric-groups
normal-subgroups
Proof that normalizer and center are subgroups
abstract-algebra
group-theory
solution-verification
normal-subgroups
How to describe all normal subgroups of the dihedral group Dn? [duplicate]
group-theory
normal-subgroups
dihedral-groups
Show that if $|G|=30$ then $G$ has normal $3$-Sylow and $5$-Sylow
group-theory
finite-groups
solution-verification
normal-subgroups
sylow-theory
Group of order $1225$ is abelian
abstract-algebra
group-theory
abelian-groups
normal-subgroups
sylow-theory
Prove that any subgroup of the center $Z(G)$ of $G$ is a normal subgroup of $G$.
abstract-algebra
group-theory
normal-subgroups
Proving that a subgroup is normal if two equivalence relations on $A$ coincide
group-theory
proof-explanation
normal-subgroups
If $N,K$ are two finite groups with isomorphic subgroups, show $ X \leq N \times K $ is normal.
group-theory
finite-groups
normal-subgroups
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