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• What is a composition series for groups? For the discussion, comment on each others posts. Find a composition series for the quaternion group Q. • A subgroup H of a group G is called characteristic if (1)(H) = H for all automorphisms (I) of G. Show that characteristic implies normal. For the discussion comment on each other posts to perfect a proof.

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Answered Same DayDec 20, 2021

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Robert answered on Dec 20 2021

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Composition Series:
It is a method for splitting up a group into simpler/smaller pieces.
For every finite group G, having order greater than one, there exists a finite series of subgroups such that,
I ∆H1∆H2∆H3 … ∆ Hs ∆G,
Where Hi-1 is a maximal subgroup of Hi and Hs ∆G denotes that Hs is a normal subgroup...

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