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New posts in finite-groups
Characterization of the isomorphic semidirect products
group-theory
finite-groups
abelian-groups
semidirect-product
Prove that there are $p+1$ points on the elliptic curve $y^2 = x^3 + 1$ over $\mathbb{F}_p$, where $p > 3$ is a prime such that $p \equiv 2 \pmod 3$.
finite-groups
modular-arithmetic
finite-fields
elliptic-curves
The product of all the elements of a finite abelian group
abstract-algebra
group-theory
finite-groups
proof-writing
How powerful is Cayley's theorem?
abstract-algebra
group-theory
finite-groups
symmetric-groups
How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$? [duplicate]
abstract-algebra
group-theory
finite-groups
proof-explanation
Can we find a bound so that we can conclude $G$ is a $p$-group?
abstract-algebra
group-theory
finite-groups
Does there exist some sort of classification of finite verbally simple groups?
abstract-algebra
group-theory
finite-groups
verbal-subgroups
characteristic-subgroups
Definition of Conjugacy Class
group-theory
finite-groups
representation-theory
Finite Groups with a subgroup of every possible index
group-theory
finite-groups
If $|H|$ and $[G:K]$ are relatively prime, then $H \leq K$
group-theory
finite-groups
If $G$ is a finite group and $|G| < |A| + |B|$, then $G=AB$.
group-theory
finite-groups
Maximum number of Sylow subgroups
abstract-algebra
group-theory
finite-groups
sylow-theory
finite subgroups of PGL(3,C)
group-theory
representation-theory
finite-groups
Proving that ${\rm Aut}(S_3)$ is isomorphic to $S_3$
abstract-algebra
group-theory
finite-groups
symmetric-groups
automorphism-group
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
group-theory
elementary-number-theory
finite-groups
p-adic-number-theory
Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple
group-theory
finite-groups
simple-groups
Classify groups of order 27
abstract-algebra
group-theory
finite-groups
p-groups
groups-enumeration
Show that left cosets partition the group
abstract-algebra
group-theory
finite-groups
Prove that $(a_1a_2\cdots a_n)^{2} = e$ in a finite Abelian group
group-theory
finite-groups
abelian-groups
How to prove that $A_5$ has no subgroup of order 30?
group-theory
finite-groups
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