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Unitary Subgroups of Commutative Group Algebras of the Characteristic Two
Ukrainian Mathematical Journal ( IF 0.5 ) Pub Date : 2020-11-21 , DOI: 10.1007/s11253-020-01829-3 Z. Balogh , V. Laver
中文翻译:
特征二的交换群代数的子群
更新日期:2020-11-22
Ukrainian Mathematical Journal ( IF 0.5 ) Pub Date : 2020-11-21 , DOI: 10.1007/s11253-020-01829-3 Z. Balogh , V. Laver
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:
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。