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
SN - 0041-5995
VL - 72
SP - 871
EP - 879
JO - Ukrainian Mathematical Journal
JF - Ukrainian Mathematical Journal
IS - 6
ER -