List questions from characteristic-subgroups

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Does group isomorphism preserve characteristics subgroups?

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Show that the identity component $G^\circ\sqsubseteq G$ (i.e., is characteristic) in a linear algebraic group $G$.

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A group may have two distinct characteristic Sylow-$p$-subgroups

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Characteristic subgroups of a group of order 6 or 12

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When the natural homomorphism from $Aut(G)$ to $Aut(G/N)$ is onto?

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If there is subgroup of finite index $n$ and $G$ is finitely generated then there is a subgroup of $G$ that has index $n$ and is characteristic in $G$

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Examples of "unexpected" characteristic subgroups

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Autocommutator subgroup is a characteristic subgroup

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All characteristic subgroups are normal

Published on 01 Apr 2015 - 9:14

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Characteristic subgroups of Aut(G)

Published on 05 Jun 2015 - 6:59

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Characteristic subgroups of non-abelian $p$-group

Published on 26 Feb 2016 - 5:30

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Characteristic Subgroups in Finite Cyclic Groups

Published on 01 Apr 2016 - 4:47

853

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Properties of Characteristic Subgroups

Published on 16 Jun 2016 - 4:31

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Normal subgroups vs characteristic subgroups

Published on 17 Aug 2011 - 21:39

List Question

When $N(N(H))=N(H)$, where $N(H)$ is the normalizer of $H$?

Does group isomorphism preserve characteristics subgroups?

Show that the identity component $G^\circ\sqsubseteq G$ (i.e., is characteristic) in a linear algebraic group $G$.

A group may have two distinct characteristic Sylow-$p$-subgroups

Characteristic subgroups of a group of order 6 or 12

When the natural homomorphism from $Aut(G)$ to $Aut(G/N)$ is onto?

If there is subgroup of finite index $n$ and $G$ is finitely generated then there is a subgroup of $G$ that has index $n$ and is characteristic in $G$

Examples of "unexpected" characteristic subgroups

Autocommutator subgroup is a characteristic subgroup

All characteristic subgroups are normal

Characteristic subgroups of Aut(G)

Characteristic subgroups of non-abelian $p$-group

Characteristic Subgroups in Finite Cyclic Groups

Properties of Characteristic Subgroups

Normal subgroups vs characteristic subgroups

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