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3-transposition group : ウィキペディア英語版 | 3-transposition group In mathematical group theory, a 3-transposition group is a group generated by a conjugacy class of involutions, called the 3-transpositions, such that the product of any two involutions from the conjugacy class has order at most 3. They were first studied by who discovered the three Fischer groups as examples of 3-transposition groups. ==History== first studied 3-transposition groups in the special case when the product of any two distinct transpositions has order 3. He showed that a finite group with this property is solvable, and has a (nilpotent) 3-group of index 2. used these groups to construct examples of non-abelian CH-quasigroups and to describe the structure of commutative Moufang loops of exponent 3.
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