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 $p$

order of non abelian group can't be what?

Show that each character of $G$ which is zero for all $g \ne 1$ is an integral multiple of the character $r_G$ of the regular representation

Can only find 2 of the 4 groups of order 2014?

If $\forall a,b \in G, \exists x \in G: a * x = b$ and $\forall a,b \in G, \exists x \in G: x * a = b$ then $G$ is a group

To construct a non-abelian group of order $55$ and $203$

How can one visualize a homomorphic mapping.

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 $H$.

Using Burnside's Lemma; understanding the intuition and theory

"Classify $\mathbb{Z}_5 \times \mathbb{Z}_4 \times \mathbb{Z}_8 / \langle(1,1,1)\rangle$"

What does it mean when people say that groups are a study of symmetry?

Is there a simple geometric example of unequal left and right cosets?

Show that a semigroup with $aS \cup \{a\} = bS \cup \{b\}$ and $Sa \cup \{a\} = Sb \cup \{b\}$ is a group

Fundamental group of Klein Bottle

If $H$ is a subgroup of a finite abelian group $G$, then $G$ has a subgroup that is isomorphic to $G/H$.

New posts in group-theory

Schur–Zassenhaus exercise: coprime subgroup contained in a complement

Is there a counterexample to this weakened converse of Hall's theorem?

understanding the commutator of dihedral group [duplicate]

Automorphisms of a Cyclic Group

Center of a quotient of a free group

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 $p$

order of non abelian group can't be what?

Show that each character of $G$ which is zero for all $g \ne 1$ is an integral multiple of the character $r_G$ of the regular representation

Can only find 2 of the 4 groups of order 2014?

If $\forall a,b \in G, \exists x \in G: a * x = b$ and $\forall a,b \in G, \exists x \in G: x * a = b$ then $G$ is a group

To construct a non-abelian group of order $55$ and $203$

How can one visualize a homomorphic mapping.

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 $H$.

Using Burnside's Lemma; understanding the intuition and theory

"Classify $\mathbb{Z}_5 \times \mathbb{Z}_4 \times \mathbb{Z}_8 / \langle(1,1,1)\rangle$"

What does it mean when people say that groups are a study of symmetry?

Is there a simple geometric example of unequal left and right cosets?

Show that a semigroup with $aS \cup \{a\} = bS \cup \{b\}$ and $Sa \cup \{a\} = Sb \cup \{b\}$ is a group

Fundamental group of Klein Bottle

If $H$ is a subgroup of a finite abelian group $G$, then $G$ has a subgroup that is isomorphic to $G/H$.