Perfect locally finite groups that are product of normal soluble subgroups of bounded derived length
Ricerche di Matematica - 2022
Tóm tắt
In the present article we consider infinite locally finite perfect groups that are product of proper normal soluble subgroups of derived length at most n (
$$\Pi {\mathfrak {S}}_n$$
-groups for short) for some fixed positive integer n and give structural results for these groups. Also we provide some consequences for certain locally finite minimal non-
$${\mathfrak {X}}$$
-groups for some classes
$${\mathfrak {X}}$$
and barely transitive groups in the context mentioned above. Furthermore, we define certain collections of groups and consider their intersection with
$$\Pi {\mathfrak {S}}_n$$
. Finally, we investigate some groups which have non-trivial minimal non-
$${\mathfrak {FC}}$$
epimorphic images.
Từ khóa
Tài liệu tham khảo
Alkış, O., Arikan, A., Arikan, A.: On groups with certain proper \(FC\)-subgroups. Algebras Represent. Theory (2021). https://doi.org/10.1007/s10468-021-10054-w
Arikan, A.: On barely transitive \(p\)-groups with soluble point stabilizer. J. Group Theory 5, 441–442 (2002)
Arikan, A.: Characterizations of minimal non-solvable Fitting-p-groups. J. Group Theory 11, 95–103 (2008)
Arikan, A., Sezer, S., Smith, H.: On locally finite minimal non-solvable groups. Central Europ. J. Math. 8, 266–273 (2010)
Arikan, A., Cutolo, G., Robinson, D.J.S.: On groups that are dominated by countably many proper subgroups. J. Algebra 509, 445–466 (2018)
Asar, A.O.: Locally nilpotent p-groups whose proper subgroups are hypercentral or nilpotent-by-Chernikov. J. Lond. Math. Soc. 61, 412–422 (2000)
Asar, A.O.: On minimal non-(residually nilpotent) locally graded groups. Mediterr. J. Math. (2021). https://doi.org/10.1007/s00009-020-01664-7
Belyaev, V.V.: On the question of existence of minimal-non-\(FC\)-groups. Siberian Math. J. 39, 1093–1095 (1998)
de Giovanni, F., Trombetti, M.: Infinite minimal non-hypercyclic groups. J. Algebra Appl. 14, No. 10 , 1550143 (2015)
de Giovanni, F., Trombetti, M.: Cohopfian groups and accessible group classes. Pac. J. Math. 312(2), 457–475 (2021)
Hartley, B.: On the normalizer condition and barely transitive permutation groups. Algebra Logic 13, 334–340 (1974)
Hartley, H., Kuzucuo\(\tilde{\text{g}}\)lu, M.: Non-simplicity of locally finite barely transitive groups, Proc. Edinburgh Math. Soc. 40, 485–490 (1997)
Kuzucuo\(\tilde{\text{ g }}\)lu, M.: Barely transitive permutation groups. Arch. Math. 55(2), 521–532 (1990)
Möhres, W.: Torsionsfreie Gruppen, deren Untergruppen alle subnormal sind. Math. Ann. 284, 245–249 (1989)
Robinson, D.J.S.: Finiteness Conditions and Generalized Soluble Groups, vol. I. II. Springer-Verlag, Berlin-Heidelberg (1972)
Wiegold, J.: Groups of finitary permutations. Arch. Math. 25, 466–469 (1974)