New posts in abelian-groups

The description of abelian Lie groups

abstract-algebra lie-groups lie-algebras abelian-groups

Let G be an abelian group, and let a∈G. For n≥1,let G[n;a] := {x∈G:x^n =a}. Show that G[n; a] is either empty or equal to αG[n] := {αg : g ∈ G[n]}... [closed]

group-theory number-theory order-theory abelian-groups cyclic-groups

Show that a nonabelian group must have at least five distinct elements [closed]

abstract-algebra group-theory abelian-groups

$\operatorname{Aut}(G)\cong \Bbb{Z}/8\Bbb{Z}$

abstract-algebra group-theory examples-counterexamples abelian-groups automorphism-group

Showing $Z(H\wr K)$, for abelian $H\neq 1$ and arbitrary $K$, is the diagonal subgroup of the base group.

group-theory abelian-groups wreath-product

Properties possessed by $H , G/H$ but not G

group-theory abelian-groups cyclic-groups normal-subgroups

Is there a good example of a subgroup of an infinitely generated abelian group that is not isomorphic to a quotient of that group?

abstract-algebra group-theory abelian-groups infinite-groups

Show $G=\langle\delta\rangle\ltimes D$ is nilpotent of class $2$.

group-theory abelian-groups semidirect-product nilpotent-groups

All subgroups normal $\implies$ abelian group

abelian-groups normal-subgroups

Why is the name "orthogonality"?

definition abelian-groups analytic-number-theory orthogonality dirichlet-character

Showing, for $G=\langle\delta\rangle\ltimes(A\times A)$ and abelian $A$, that $Z(G)=G'\cong A$.

group-theory abelian-groups semidirect-product

Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?

group-theory abelian-groups group-homomorphism infinite-groups

Subgroups of $\Bbb{R}^n$ that are closed and discrete

group-theory lie-groups lie-algebras abelian-groups

Computing easy direct limit of groups

abstract-algebra group-theory category-theory abelian-groups

infinite abelian group where all elements have order 1, 2, or 4

group-theory abelian-groups p-groups

Showing that a cyclic automorphism group makes a finite group abelian

group-theory abelian-groups cyclic-groups automorphism-group

When will a group be Abelian?

abstract-algebra group-theory abelian-groups big-list

Why are abelian groups of interest? What is their usefulness?

abstract-algebra group-theory abelian-groups motivation

Is there a topological group that is connected but not path-connected?

abelian-groups topological-groups connectedness uniform-spaces

Subgroups of a finitely generated abelian group without torsion

finite-groups abelian-groups