Newbetuts

Let G be an abelian group, and let a∈G. For n≥1,let G[n;a] := {x∈G:x^n =a}. Show that G[n; a] is either empty or equal to αG[n] := {αg : g ∈ G[n]}... [closed]

Prove that for prime $p \gt 2$, $(p - 1)^{p - 1} \equiv p+1 \pmod{p^2}$.

Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$

Find all homomorphisms from $\mathbb{Z_{12}}$ to $\mathbb{Z_{18}}$ [duplicate]

Can you find an element of order 10 in $\mathbb{Z}_{31}^{*}$

Showing that for $G = \langle x \rangle$ if $|G|$ is odd, then $\phi$ is an injection.

Fibonacci Sequence in $\mathbb Z_n$.

Proving Schur-Zassenhaus Theorem, with added assumption that $G/H$ is cyclic

Intuition and Tricks - Crafty Short Proof - Generators, Order of a Cyclic Group - Fraleigh p. 64 Theorem 6.14

Properties possessed by $H , G/H$ but not G

Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic

At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic [closed]

In a finite cyclic group, the generator has the order of the group

Showing that a cyclic automorphism group makes a finite group abelian

Prove a certain cyclic extension with prime power order is simple

Visualized group tables for $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$

New posts in cyclic-groups

Is there some sort of classification of all minimal non-cyclic groups?

Semidirect product of two cyclic groups

Quadratic subfield of cyclotomic field [duplicate]

Homomorphism between cyclic groups

Let G be an abelian group, and let a∈G. For n≥1,let G[n;a] := {x∈G:x^n =a}. Show that G[n; a] is either empty or equal to αG[n] := {αg : g ∈ G[n]}... [closed]

Prove that for prime $p \gt 2$, $(p - 1)^{p - 1} \equiv p+1 \pmod{p^2}$.

Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$

Find all homomorphisms from $\mathbb{Z_{12}}$ to $\mathbb{Z_{18}}$ [duplicate]

Can you find an element of order 10 in $\mathbb{Z}_{31}^{*}$

Showing that for $G = \langle x \rangle$ if $|G|$ is odd, then $\phi$ is an injection.

Fibonacci Sequence in $\mathbb Z_n$.

Proving Schur-Zassenhaus Theorem, with added assumption that $G/H$ is cyclic

Intuition and Tricks - Crafty Short Proof - Generators, Order of a Cyclic Group - Fraleigh p. 64 Theorem 6.14

Properties possessed by $H , G/H$ but not G

Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic

At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic [closed]

In a finite cyclic group, the generator has the order of the group

Showing that a cyclic automorphism group makes a finite group abelian

Prove a certain cyclic extension with prime power order is simple

Visualized group tables for $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$