Newbetuts

If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$? [duplicate]

Countable number of subgroups $\implies $ countable group

On which structures does the free group 'naturally' act?

Is there a good example of a subgroup of an infinitely generated abelian group that is not isomorphic to a quotient of that group?

Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?

Is there a group $G$ and subgroup $H$, such that there exists $g\in G$ with $gHg^{-1} \subset H$ and $|H:gHg^{-1}|$ is infinite?

Can an uncountable group have a countable number of subgroups?

There exist infinite solvable $p$-groups with trivial centre. (Use a hint.)

Examples of Infinite Simple Groups

If ratio: number of integers in between twin primes to number of all integers approaches but never reaches zero, does it imply infinite twin primes? [closed]

Finitely presented group with fewer relations than generators.

The number of elements of order $2$ in an infinite group

Is every subgroup of infinite Boolean group finite?

Find an abelian infinite group such that every proper subgroup is finite

Is it possible that a left coset of $H$ contains more than one right coset of $H$?

Probability of selecting an even natural number from the set $\Bbb N$.

Does there exist any uncountable group , every proper subgroup of which is countable?

New posts in infinite-groups

Does every infinite group have a maximal subgroup?

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

Groups with finite automorphism groups.

If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$? [duplicate]

Countable number of subgroups $\implies $ countable group

On which structures does the free group 'naturally' act?

Is there a good example of a subgroup of an infinitely generated abelian group that is not isomorphic to a quotient of that group?

Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?

Is there a group $G$ and subgroup $H$, such that there exists $g\in G$ with $gHg^{-1} \subset H$ and $|H:gHg^{-1}|$ is infinite?

Can an uncountable group have a countable number of subgroups?

There exist infinite solvable $p$-groups with trivial centre. (Use a hint.)

Examples of Infinite Simple Groups

If ratio: number of integers in between twin primes to number of all integers approaches but never reaches zero, does it imply infinite twin primes? [closed]

Finitely presented group with fewer relations than generators.

The number of elements of order $2$ in an infinite group

Is every subgroup of infinite Boolean group finite?

Find an abelian infinite group such that every proper subgroup is finite

Is it possible that a left coset of $H$ contains more than one right coset of $H$?

Probability of selecting an even natural number from the set $\Bbb N$.

Does there exist any uncountable group , every proper subgroup of which is countable?