On some realizable metabelian 5-groups

Fouad Elmouhib; Mohamed Talbi; Abdelmalek Azizi

doi:10.5269/bspm.62708

Fouad Elmouhib Mohammed Premier University https://orcid.org/0000-0002-9880-3236
Mohamed Talbi Regional Center of Education and Training
Abdelmalek Azizi Mohammed Premier University https://orcid.org/0000-0002-0634-1995

Résumé

Let G be a 5-group of maximal class and G' = [G, G] its derived group. Assume that the abelianization G/G' is of type (5, 5) and the transfers from H1 to G' and from H2 to G' are trivial, where H1 and H2 are two maximal normal subgroups of G. Then G is completely determined with the isomorphism class groups of maximal class. Moreover the group G is realizable with some fields k, which is the normal closure of a pure quintic field.

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Bibliographies de l'auteur

Fouad Elmouhib, Mohammed Premier University

Department of Mathematics and Computer Sciences, Mohamed 1st University,
Oujda - Morocco.

Mohamed Talbi, Regional Center of Education and Training

Regional Center of Professions of Education and Training in the Oriental, Oujda - Morocco.

Abdelmalek Azizi, Mohammed Premier University

Department of Mathematics and Computer Sciences, Mohamed 1st University,
Oujda - Morocco.

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The PARI Group, Version 2.4.9, Bordeaux, 2017, http://pari.math.u-bordeaux.fr.