Newbetuts
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New posts in abelian-groups
Lang Lemma 6.1 (before Sylow): if $p$ divides order of finite abelian group, then subgroup with $p$ order exists. Why is $x^s\neq1$ guaranteed?
abstract-algebra
group-theory
finite-groups
abelian-groups
Whence this generalization of linear (in)dependence?
abstract-algebra
modules
abelian-groups
A condition for a subgroup of a finitely generated free abelian group to have finite index
abstract-algebra
group-theory
abelian-groups
Explanation why an abelian tower admits a cyclic refinement
abstract-algebra
group-theory
finite-groups
abelian-groups
cyclic-groups
Finding the order of the automorphism group of the abelian group of order 8.
linear-algebra
abstract-algebra
group-theory
finite-groups
abelian-groups
Abelian group admitting a surjective homomorphism onto an infinite cyclic group
abstract-algebra
group-theory
abelian-groups
cyclic-groups
The center of a group is an abelian subgroup
abstract-algebra
group-theory
abelian-groups
Relation between the index of a group and its center and the order of the commutator
group-theory
representation-theory
abelian-groups
characters
If Cylic subgroup implies abelian implies normal then how A5 is simple group [closed]
group-theory
abelian-groups
normal-subgroups
cyclic-groups
sylow-theory
Do both versions (invariant and primary) of the Fundamental Theorem for Finitely Generated Abelian Groups hold at the same time?
abstract-algebra
group-theory
ring-theory
modules
abelian-groups
Why are there $12$ automorphisms of $\Bbb Z\oplus \Bbb Z_{3}$?
abstract-algebra
group-theory
finite-groups
abelian-groups
Prove every group of order less or equal to five is abelian [closed]
abstract-algebra
group-theory
abelian-groups
normal-subgroups
What is a coset?
abstract-algebra
group-theory
abelian-groups
How to find subgroups of $ \;\;\Bbb Z_2\times \Bbb Z_6$
abstract-algebra
group-theory
abelian-groups
cyclic-groups
Quotient of two free abelian groups of the same rank is finite?
group-theory
abelian-groups
free-groups
Is it true that a dihedral group is nonabelian?
abstract-algebra
group-theory
abelian-groups
dihedral-groups
$G$ abelian group with $\vert G\vert =mn$ and $\gcd(m,n)=1$.
group-theory
finite-groups
abelian-groups
Are inverses of groups unique in general?
abstract-algebra
group-theory
inverse
abelian-groups
What does it mean that "the action of $\mathbb{Z}$ on $M$ factors through the quotient $\mathbb{Z}/p^n \mathbb{Z}$"?
number-theory
commutative-algebra
modules
abelian-groups
group-actions
Finite Abelian groups: $G \times H \cong G\times K$ then $H\cong K$
abstract-algebra
group-theory
finite-groups
abelian-groups
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