TY - JOUR

T1 - Unitary Subgroups of Commutative Group Algebras of the Characteristic Two

AU - Balogh, Z.

AU - Laver, V.

N1 - Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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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U2 - 10.1007/s11253-020-01829-3

DO - 10.1007/s11253-020-01829-3

M3 - Article

AN - SCOPUS:85093081414

VL - 72

SP - 871

EP - 879

JO - Ukrainian Mathematical Journal

JF - Ukrainian Mathematical Journal

SN - 0041-5995

IS - 6

ER -