Abstract
Lower-modular infinite groups are considered in this paper. We give a generalization of a theorem of Jones and Ito to locally finite groups and to nilpotent-by-abelian groups; moreover we study periodic subgroups of lower-modular groups.
Similar content being viewed by others
Bibliografia
Baer R.,Nilpotent groups and their generalizations, Trans. Amer. Math. Soc.,47 (1940), 393–434.
Baer R.,Überauflösbare Gruppen, Abh. Math. Sem. Univ. Hamburg,23 (1957), 11–28.
Baer R.,Irreducible groups of automorphisms of abelian groups, Pacific J. Math.,14 (1964), 385–406.
Franchetta A.,Alcune osservazioni sui gruppi i cui sottogruppi massimali hanno indici primi, Rend. Accad. Sci. Fis. Mat. Napoli,45 (1978), 453–462.
Ito N.,Note on LM-groups of finite order, Kodai Math. Sem. Reports (1951), 1–6.
Jones A. W.,Semimodular finite groups and the Burnside basis theorem, Bull. Amer. Math. Soc.,52 (1946).
Phillips R. E.—Robinson D. J. S.—Roseblade J. E.,Maximal subgroups and chief factors of certain generalized soluble groups, Pacific J. Math.,37 (1971), 475–480.
Robinson D. J. S.,A theorem on finitely generated hyperabelian groups, Invent. Math.,10 (1970), 38–43.
Robinson D. J. S.,Finiteness conditions and generalized soluble groups, Springer 1972.
Schenkman E.,Group theory, Van Nostrand Company 1965.
Schmidt R.,Modulare Untergruppen endlicher Gruppen, Illinois J. Math.,13 (1969), 358–377.
Suzuki M.,Structure of a group and the structure of its lattice of subgroups, Springer 1956.
Zappa G.,Sui gruppi di Hirsch supersolubili I, Rend. Sem. Mat. Univ. Padova,12 (1941), 1–11.
Author information
Authors and Affiliations
Additional information
Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R. (1980–81).
Rights and permissions
About this article
Cite this article
De Giovanni, F., Franciosi, S. Sui gruppi sottomodulari infiniti. Rend. Circ. Mat. Palermo 31, 257–266 (1982). https://doi.org/10.1007/BF02844358
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02844358