NETMaths
The bookUnit 2 · Groups39 / 83

Normal subgroups, quotients, isomorphism theorems

Why this is asked: Normality is not transitive. Know the standard normal/non-normal examples in S₄ and A₄, and that index-2 subgroups are always normal.

Normal subgroups, quotients and the isomorphism theorems

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The first isomorphism theorem, used as a toolinteractive

Three quotients identified in one line each — the fastest way to answer 'what is G/N?'

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The trap here

“Converse of Lagrange: d | |G| ⇒ subgroup of order d” — false

A4A_{4} has no subgroup of order 6

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Check yourself — select all that apply

Which of the following statements are true?

Next: Permutation groups: cycles, sign, conjugacy in S_n and A_n

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Open this in the full syllabus view · Unit 2