Groups with sign structure and their antiautomorphisms (Q1201250)

A group with sign structure is a group \(G\) in which each element \(x\) is given a sign \(| x| \in \{-1,1\}\) subject to the condition \(| xy| = | x| | y|\) for every \(x\) and \(y\) in \(G\). The paper is organized as follows. Section 2 is devoted to elementary properties of groups with sign structure and their antiautomorphisms. In the next section groups with sign structure are characterized in the language of extensions of groups by \(\mathbb{Z}_ 2\). The final section contains a complete description of antiautomorphisms in terms of certain extensions of automorphisms.