Plasma effect: Difference between revisions
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Given a group, there are some subgroups of interest that can be defined uniquely and functionally in terms of <math>G</math>, such as the center, commutator, etc. These should be invariant under isomorphisms, that is, any isomorphism on the groups, must induce a corresponding isomorphism on the subgroups. Hence, such subgroups are invariant under automorphisms, and are always [[characteristic subgroup]]s. | |||
[[Category:Group theory]] | |||
Revision as of 14:25, 20 October 2013
Given a group, there are some subgroups of interest that can be defined uniquely and functionally in terms of , such as the center, commutator, etc. These should be invariant under isomorphisms, that is, any isomorphism on the groups, must induce a corresponding isomorphism on the subgroups. Hence, such subgroups are invariant under automorphisms, and are always characteristic subgroups.
