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New posts in group-isomorphism
$GL(n, \mathbb{C})$ is isomorphic to a subgroup of $GL(2n, \mathbb{R})$
abstract-algebra
group-theory
group-isomorphism
general-linear-group
Concerning Groups having the property that intersection of any two non-trivial subgroups is non-trivial
group-theory
reference-request
group-isomorphism
direct-product
Determining the proper function for morphisms
abstract-algebra
group-isomorphism
Let $\phi:\Bbb{Z}_{20} \to \Bbb{Z}_{20}$ be an automorphism and $\phi(5)=5$. What are the possibilities of $\phi(x)$?
finite-groups
group-isomorphism
automorphism-group
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
group-theory
solution-verification
abelian-groups
group-isomorphism
automorphism-group
Is $\Bbb R/\Bbb Z$ isomorphic to $\Bbb R/2\Bbb Z$?
group-isomorphism
quotient-group
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
abstract-algebra
group-theory
finite-groups
group-isomorphism
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
abstract-algebra
group-theory
group-isomorphism
Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition.
group-theory
group-isomorphism
$U(n) \simeq \frac{SU(n) \times U(1)}{\mathbb{Z}_{n}}$ isomorphism
group-theory
group-isomorphism
Prove $A$, the set of all complex numbers with modulus $1$, is a subgroup of $\Bbb C^*$. Prove also that $\Bbb C^*\cong\Bbb R^+\times A$.
complex-analysis
group-theory
group-isomorphism
How far can we go with group isomorphisms?
abstract-algebra
group-theory
group-isomorphism
Why is it true that $|AB:A|=|B:A\cap B|$ even if $A$ is not normal in $AB$? (Second Isomorphism Theorem)
abstract-algebra
group-theory
group-isomorphism
In general, what techniques can be used to show that 2 groups are not isomorphic?
abstract-algebra
group-theory
group-isomorphism
Proving a set of automorphisms of a group is a group under composition
abstract-algebra
group-isomorphism
Finding a subgroup of $S_8$ isomorphic to $\mathbb{Z}_4 \times \mathbb{Z}_4$
abstract-algebra
group-theory
solution-verification
symmetric-groups
group-isomorphism
When are two direct products of groups isomorphic?
abstract-algebra
group-theory
group-isomorphism
A group $G$ isomorphic to $\mathcal{P}(A)$ [duplicate]
abstract-algebra
group-theory
group-isomorphism
Prove $\mathbb{Z}_4\ncong \mathbb{Z}_2\times\mathbb{Z}_2$
abstract-algebra
group-theory
solution-verification
finite-groups
group-isomorphism
Does an isomorphism of groups that can be written as a direct product induce isomorphisms on the factors?
abstract-algebra
group-theory
group-isomorphism
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