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New posts in finite-groups
Characterization of nilpotency with normal subgroups
group-theory
finite-groups
normal-subgroups
nilpotent-groups
Number of homomorphisms between two arbitrary groups
abstract-algebra
group-theory
finite-groups
group-homomorphism
permutation-cycles
Do all representations of finite groups have one-dimensional subrepresentations?
representation-theory
finite-groups
Find the number of homomorphisms between cyclic groups.
abstract-algebra
group-theory
finite-groups
cyclic-groups
Expression of unitary group , the discrete subgroups and invariants
abstract-algebra
algebraic-topology
finite-groups
lie-groups
lie-algebras
Let $N$ be a normal subgroup of index $m$ in $G$. Prove that $a^m \in N$ for all $a \in G$.
abstract-algebra
group-theory
finite-groups
Show every subgroup of D4 can be regarded as an isotropy group for a suitable action of D4
group-theory
finite-groups
What is the order of $2$ in $(\mathbb{Z}/n\mathbb{Z})^\times$?
group-theory
elementary-number-theory
finite-groups
Groups with Same Number Of Elements and Subgroups
group-theory
finite-groups
Can we find element of order $q^2-1$ in $\text{GL}_2(\mathbb{F}_q)$?
abstract-algebra
group-theory
finite-groups
finite-fields
general-linear-group
Which non-Abelian finite groups contain the two specific centralizers? - part II
abstract-algebra
group-theory
discrete-mathematics
finite-groups
representation-theory
What is known about the numbers $M_p = \left\vert C(\mathbb{F}_p )\right\vert$?
number-theory
finite-groups
finite-fields
elliptic-curves
Every group of order $150$ has a normal subgroup of order $25$
abstract-algebra
group-theory
finite-groups
sylow-theory
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
abstract-algebra
finite-groups
cyclic-groups
totient-function
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
How many elements have to verify the associativity property in a group?
group-theory
finite-groups
associativity
Does there exist some sort of classification of incompressible groups?
abstract-algebra
group-theory
finite-groups
symmetric-groups
group-actions
Every normal subgroup of a finite group is contained in some composition series
abstract-algebra
group-theory
finite-groups
simple-groups
Noncyclic Abelian Group of order 51
abstract-algebra
group-theory
finite-groups
For which numbers $n$ is every group of order $n$ nilpotent?
group-theory
finite-groups
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