Newbetuts

Suppose $K/F$ is a Galois extension of degree $p^m$. Then there is a chain of extensions $F \subseteq F_1 \subseteq \cdots F_m = K$ each of degree $p$

Let G be a finite group, $H \triangleleft G$ be a normal subgroup and $S$ be a Sylow subgroup of $G$. Show that $H \cap S$ is a Sylow subgroup of $H$.

Decomposition of finitely-generated abelian group

A group of order $30$ has a normal $5$-Sylow subgroup.

If $N\lhd G$ then $n_p(G/N) \leq n_p(G)$.

If Cylic subgroup implies abelian implies normal then how A5 is simple group [closed]

Normalizer of a Sylow 2-subgroups of dihedral groups

Understanding the normalizer of a Sylow $p$-subgroup

Sylow Subgroups of a Dihedral Group

Direct product of Sylow subgroups

All non abelian groups of order $56$, when $\mathbb Z_7\triangleleft G$

How many subgroups of order 17 does $S_{17}$ have?

If $|G|=36$ then $G$ has either a normal $2$-Sylow or a normal $3$-Sylow

Intuition behind picking group actions and Sylow

New posts in sylow-theory

Find a $2$-Sylow subgroup of $\mathrm{GL}_3(F_7)$

Group of order 30 can't be simple

Classifying groups of order 21.

Prove that a non-abelian group of order $pq$ ($p<q$) has a nonnormal subgroup of index $q$

Finding Sylow 2-subgroups of the dihedral group $D_n$

Normalizer and centralizer are equivalent when $p$ is the smallest prime dividing $|G|$

Suppose $K/F$ is a Galois extension of degree $p^m$. Then there is a chain of extensions $F \subseteq F_1 \subseteq \cdots F_m = K$ each of degree $p$

Let G be a finite group, $H \triangleleft G$ be a normal subgroup and $S$ be a Sylow subgroup of $G$. Show that $H \cap S$ is a Sylow subgroup of $H$.

Decomposition of finitely-generated abelian group

A group of order $30$ has a normal $5$-Sylow subgroup.

If $N\lhd G$ then $n_p(G/N) \leq n_p(G)$.

If Cylic subgroup implies abelian implies normal then how A5 is simple group [closed]

Normalizer of a Sylow 2-subgroups of dihedral groups

Understanding the normalizer of a Sylow $p$-subgroup

Sylow Subgroups of a Dihedral Group

Direct product of Sylow subgroups

All non abelian groups of order $56$, when $\mathbb Z_7\triangleleft G$

How many subgroups of order 17 does $S_{17}$ have?

If $|G|=36$ then $G$ has either a normal $2$-Sylow or a normal $3$-Sylow

Intuition behind picking group actions and Sylow