Finite Group Theory

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4 domain-specific abstractions whose origin domain is Finite Group Theory.

• 3-transposition group — A group generated by a conjugacy class of involutions such that the product of any two generators has order at most three.
• 3D4 — A twisted family of groups of Lie type obtained from type D4 by combining its order-three triality automorphism with a cubic field automorphism.
• Diameter (group theory) — The largest Cayley-graph distance required to reach elements of a finite group under a specified generating-set convention, sometimes maximized over all generating sets.
• Thompson factorization — A factorization of certain finite groups as a product of two structurally selected subgroups, commonly normalizers or centralizers of p-subgroups.