On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup
Publish place: International Journal of Group Theory، Vol: 11، Issue: 1
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_THEGR-11-1_005
تاریخ نمایه سازی: 19 آبان 1400
Abstract:
We study soluble groups G in which each subnormal subgroup H with infinite rank is commensurable with a normal subgroup, i.e. there exists a normal subgroup N such that H\cap N has finite index in both H and N. We show that if such a G is periodic, then all subnormal subgroups are commensurable with a normal subgroup, provided either the Hirsch-Plotkin radical of G has infinite rank or G is nilpotent-by-abelian (and has infinite rank).
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Authors
Ulderico Dardano
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Via Cintia - Monte S. Angelo, I-۸۰۱۲۶ Napoli, Italy
Fausto De Mari
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Via Cintia - Monte S. Angelo, I-۸۰۱۲۶ Napoli, Italy