首页|The unitary subgroups of group algebras for a class of finite 2-groups with the derived subgroup of order 2
The unitary subgroups of group algebras for a class of finite 2-groups with the derived subgroup of order 2
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Let p be a prime and F be a finite field of characteristic p.Suppose that FG is the group algebra of the finite p-group G over the field F.Let V(FG)denote the group of normalized units in FG and let V*(FG)denote the unitary subgroup of V(FG).If p is odd,then the order of V*(FG)is|F|(|G|-1)/2.However,the case p=2 still is open.In this paper,the order of V*(FG)is computed when G is a nonabelian 2-group given by a central extension of the form 1 → Z2n ×Z2m → G → Z2 ×…× Z2 →1 and G'(≌)Z2,n,m≥1.Furthermore,a conjecture is confirmed,i.e.,the order of V*(FG)can be divisible by|F|1/2(|G|+|Ω1(G)|)-1,where Ω1(G)={g ∈ G|g2=1}.
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