New posts in finite-groups

Characterization of the isomorphic semidirect products

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 $p \equiv 2 \pmod 3$.

The product of all the elements of a finite abelian group

How powerful is Cayley's theorem?

How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$? [duplicate]

Can we find a bound so that we can conclude $G$ is a $p$-group?

Does there exist some sort of classification of finite verbally simple groups?

Definition of Conjugacy Class

Finite Groups with a subgroup of every possible index

If $|H|$ and $[G:K]$ are relatively prime, then $H \leq K$

If $G$ is a finite group and $|G| < |A| + |B|$, then $G=AB$.

Maximum number of Sylow subgroups

finite subgroups of PGL(3,C)

Proving that ${\rm Aut}(S_3)$ is isomorphic to $S_3$

Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$

Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple

Classify groups of order 27

Show that left cosets partition the group

Prove that $(a_1a_2\cdots a_n)^{2} = e$ in a finite Abelian group

How to prove that $A_5$ has no subgroup of order 30?