1977/01/01 by Jeffrey S. Leon, Charles C. Sims · 1 citation
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #semigroups and automata theory #Uniqueness #Simple (philosophy) #Mathematics #Group (periodic table) #Simple group #Combinatorics #Pure mathematics #Mathematical analysis #Physics #Philosophy #Epistemology
paper · pdf · doi:10.1090/s0002-9904-1977-14369-3
openalex publication_date 1977/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently Fischer [1] discovered three finite simple groups each of which contains a conjugacy class D of involutions such that for all x and y in D the order of the product xy is 1, 2, or 3. Such a class is called a class of 3-transpositions. More generally, if n is a set of positive integers and D is a conjugacy class of involutions in the finite group G, then D is said to be a class of 7r-transpositions in G if D generates G and for all noncommuting elements x and y of D the order of xy is in ir. Fischer has produced evidence suggesting the existence of a new simple group containing a class of 3, 4-transpositions. Fischer determined a number of properties of the group, including its order, which is