Locally graded groups with many (locally nilpotent)-by-Chernikov subgroups

ATLIHAN, SEVGİ; Badis, Abdelhafid; Dilmi, Amel; Trabelsi, Nadir

doi:10.1007/s10474-026-01609-8

Locally graded groups with many (locally nilpotent)-by-Chernikov subgroups

ATLIHAN S., Badis A., Dilmi A., Trabelsi N.

Acta Mathematica Hungarica, 2026 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Basım Tarihi: 2026
Doi Numarası: 10.1007/s10474-026-01609-8
Dergi Adı: Acta Mathematica Hungarica
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
Anahtar Kelimeler: Baer groups, Locally (soluble-by-finite), Locally graded, Locally nilpotent, Rank
Gazi Üniversitesi Adresli: Evet

Özet

In this work we prove that a locally graded group whose proper subgroups are (locally nilpotent)-by-Chernikov is itself (locally nilpotent)-by-Chernikov. We prove also that if G is an X -group of infinite rank whose proper subgroups of infinite rank are (locally nilpotent)-by-Chernikov (respectively, Baer-by-Chernikov), then so is G; where X is the class defined by N. S. Chernikov as the closure of the class of periodic locally graded groups by the closure operations P´,P` and L.