Explicit construction of \(2S_ n\) Galois extensions
The author considers the construction of explicit solutions to the embedding problems given by 2G\(\to G\simeq Gal(L/K)\), where G is a subgroup of the symmetric group \(S_ n\), 2G is the preimage of G in either of the two stem covers of \(S_ n\); K is a field of characteristic different from 2 and L/K is a Galois extension with Galois group G. The author reduces this embedding problem to an \(A_ n\)-type embedding problem, where \(\tilde A_ n\) is the double cover of the alternating group \(A_ n\). Then, she uses the explicit solution obtained in her previous paper [J. Algebra 127, 452-461 (1989; see the preceding review)] to reach an explicit formula for the present embedding problem. Moreover, an alternative method of resolution is given in order to simplifie effective computations, in the case \(2^+S_ n\).
scientific article; zbMATH DE number 4154558