On finite "p"-groups with cyclic characteristic series

• Autores: Piroska Lakatos
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 74, Fasc. 1-2, 2009, págs. 187-193
• Idioma: inglés
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• Resumen

  • Let G be a ¯nite p-group having a characteristic cyclic series (c.c.s.) and let © be its Frattini subgroup. It is shown that the automorphism group of G is either a p-group or is the semidirect product of a normal p-Sylow subgroup of G by an elementary abelian group of exponent p ¡ 1 and of order (p ¡ 1)r, where 1 · r · s and s = jG=©j. It is also shown that G has a c.c.s. containing ©.