We aim to study maximal pairwise commuting sets of 3-transpositions(trans-vections)of the simple unitary group Un(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=Un(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-(v,k,λ)designs D=(P,B),with P=D and B={Lg | 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 U4(2),U5(2),U6(2),U7(2),U8(2)and U9(2).
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