Group structure

Element orders, normal subgroups and quotients, solvability, Sylow subgroups, and composition series.

Cauchy’s theorem: elements of prime order

Cauchy's theorem: elements of prime order

Abel-Ruffini and solvable groups: why S_5 blocks the quintic

Abel-Ruffini and solvable groups: why S_5 blocks the quintic

Sylow’s theorems in S_4

Sylow's theorems in S_4

Hölder’s quotient groups: S_4 / V_4 is S_3

Hölder's quotient groups: S_4 / V_4 is S_3

Jordan-Hölder: composition series and their factors

Jordan-Hölder: composition series and their factors