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 trap here
“Converse of Lagrange: d | |G| ⇒ subgroup of order d” — false
has no subgroup of order 6
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