Abstract
AbstractLetFbe a field of characteristic two andGa finite abelian 2-group with an involutory automorphismη. IfG=H×Dwith non-trivial subgroupsHandDofGsuch that η inverts the elements ofH(Hwithout a direct factor of order 2) and fixesDelement-wise, then the linear extension ofηto the group algebraFGis called anice involution. This determines the groups of unitary and symmetric normalized units ofFG. We calculate the orders and the invariants of these subgroups.
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