Basic 3-Transposittions of Unitary Group Un(2)  

作　　者：J.Moori 

机构地区：[1]School of Mathematical and Physical Sciences North-West University(Mafikeng),Mmabatho 2735,South Africa

出　　处：《Algebra Colloquium》2023年第1期31-42,共12页代数集刊（英文版）

摘　　要：We aim to study maximal pairwise commuting sets of 3-transpositions(transvections)of the simple unitary group U_(n)(2)over GF(4),and to construct designs from these sets.Any maximal set of pairwise commuting 3-transpositions is called a basic set of transpositions.Let G=U_(n)(2).It is well known that G is a 3-transposition group with the set D,the conjugacy class consisting of its transvections,as the set of 3-transpositions.Let L be a set of basic transpositions in D.We give general descriptions of L and 1-(ν,κ,λ)designs D=(P,B),with P=D and B={L^(9)|g∈G}.The parameters k=|L|,λ and further properties of D are determined.We also,as examples,apply the method to the unitary simple groups U_(4)(2),U_(5)(2),U_(6)(2),U_(7)(2),U_(8)(2)and U_(9)(2).

关 键 词：DESIGNS simple groups unitary groups 3-transposition groups basic transposition commuting sets transvections 

分 类 号：O17[理学—数学]