What is the intuition behind the solvable groups? It is defined by composition series. Is there any intuitive way to understand it?
2026-04-07 09:21:39.1775553699
Solvability of a group
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Evariste Galois' work was motivated by the behavior of roots of polynomial equations - could they be solved by radicals? It turned out that he had to develop group theory and especially part of the theory of solvable groups, which directy relates to the solvability of polynomial equations by radicals. There is a slew of literature on this subject - a nice book to start with is written by Ian Stewart - http://math.illinoisstate.edu/schebol/teaching/407-14-files/Stewart-galois_theory.pdf