Let FG be the group algebra of a finite 2-group G over a finite field F of characteristic two and let ⊛ be an involution that arises from G. The ⊛-unitary subgroup of FG is denoted by V_⊛(FG) and defined as the set of all normalized units u satisfying the property u^⊛ = u⁻¹. We establish the order of V_⊛(FG) for all involutions ⊛ arising from G, where G is a finite cyclic 2-group, and show that all ⊛-unitary subgroups of FG are not isomorphic.

中文翻译：

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特征二的交换群代数的子群

让FG是有限2基团组成的组代数ģ在有限域˚F的特性两让⊛是从产生对合G.的⊛统一的亚组FG被表示为V _⊛（FG）和定义为集合所有的标准化单位ü满足性能ü ^⊛  =  ü ^-1 。我们建立的顺序V _⊛（FG从产生的所有对合⊛）G，其中G ^是一个有限循环的2群，表明FG的所有⊛sub子群不是同构的。