A note on groups paralyzing a subgroup series |
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| Authors: | Ulderico Dardano Clara Franchi |
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| Institution: | (1) Dipartimento di Matematica e Appl. “R. Caccioppoli”, Università di Napoli “Federico II”, Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy;(2) Dipartimento di Matematica Pura e Applicata, Università degli Studi di Padova, Via Belzoni 7, I-35131 Padova, Italy |
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| Abstract: | We consider groups Γ of automorphisms of a groupG acting by means of power automorphisms on the factors of a normal series inG with lengthm. We show that G, Γ] is nilpotent with class at mostm and that this bound is best possible. Moreover, such a Γ is parasoluble with paraheight at most 1/2m(m+3)+1, provided Γ′ is periodic. We give best possible bound in the case where the series is a central one. |
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| Keywords: | Supersoluble group parasoluble group power automorphism |
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