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Unitary Subgroups of Commutative Group Algebras of the Characteristic Two

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. United Arab Emirates University, Al Ain, UAE

    Z. Balogh

  2. Uzhhorod National University, Uzhhorod, Ukraine

    V. Laver

Authors
  1. Z. Balogh
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  2. V. Laver
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Correspondence to V. Laver.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 6, pp. 751–757, June, 2020. Ukrainian DOI: 10.37863/umzh.v72i6.1068.

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Balogh, Z., Laver, V. Unitary Subgroups of Commutative Group Algebras of the Characteristic Two. Ukr Math J 72, 871–879 (2020). https://doi.org/10.1007/s11253-020-01829-3

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  • DOI: https://doi.org/10.1007/s11253-020-01829-3

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