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On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup | ||
| International Journal of Group Theory | ||
| دوره 11، شماره 1، خرداد 2022، صفحه 37-42 اصل مقاله (187.72 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2021.127143.1671 | ||
| نویسندگان | ||
| Ulderico Dardano* ؛ Fausto De Mari | ||
| Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Via Cintia - Monte S. Angelo, I-80126 Napoli, Italy | ||
| چکیده | ||
| 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). | ||
| کلیدواژه‌ها | ||
| transitivity؛ core-finite؛ normal-by-finite؛ close to normal | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 354 تعداد دریافت فایل اصل مقاله: 159 |
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