The authors continue their investigation of \$S\$-groups, i.e. the groups \$G\$, in which every subgroup \$H\$ is \$f\$-subnormal (there exists an \$f\$-series from \$H\$ to \$G\$, that is a finite series \$H=H_0\le H_1\le\cdots\le H_n=G\$ such that \$|H_i:H_{i-1}|\$ is finite or \$H_{i-1}\$ is normal in \$H_i\$).\par The main results of the article are the following theorems: Theorem 1. A torsion \$S\$-groups is an extension of a finite group by a group in which all subgroups are subnormal. Theorem 2. The primary components of the subgroup generated by the nilpotent residuals of the finitely generated subgroups of an \$S\$-group \$G\$ are finite. [Igor Subbotin (Los Angeles)]

### Groups with all subgroups \$f\$-subnormal

#### Abstract

The authors continue their investigation of \$S\$-groups, i.e. the groups \$G\$, in which every subgroup \$H\$ is \$f\$-subnormal (there exists an \$f\$-series from \$H\$ to \$G\$, that is a finite series \$H=H_0\le H_1\le\cdots\le H_n=G\$ such that \$|H_i:H_{i-1}|\$ is finite or \$H_{i-1}\$ is normal in \$H_i\$).\par The main results of the article are the following theorems: Theorem 1. A torsion \$S\$-groups is an extension of a finite group by a group in which all subgroups are subnormal. Theorem 2. The primary components of the subgroup generated by the nilpotent residuals of the finitely generated subgroups of an \$S\$-group \$G\$ are finite. [Igor Subbotin (Los Angeles)]
##### Scheda breve Scheda completa Scheda completa (DC)
2001
8879993453
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11390/677443`
##### Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

##### Citazioni
• ND
• ND
• ND