Relative projective monomial groups
Clifford's theory for linear representations (or characters) is generally very well known; see for instance Chapter 6 in \textit{I. M. Isaacs}' book ``Character theory of finite groups'' [Dover, New York (1994; Zbl 0849.20004)]. It is of some importance to know whether \(\chi\in\text{Irr}(G)\) satisfies \(\vartheta^G=\chi\) and \(\vartheta_N\in\text{Irr}(N)\), where \(N\) is a normal subgroup of \(G\). If so, we say that \(\chi\) is a relative monomial character with respect to \(N\).NEWLINENEWLINENEWLINEIn this paper things are recasted in the realm of projective Clifford theory and so-called relative projective monomial characters with respect to a normal subgroup. Things run certainly not so smoothly as in the linear representations case, and the results obtained are an important contribution to extend well-established results on monomial characters to results on projective monomial characters.
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