Infinite locally finite simple groups with many complemented subgroups

Ferrara, Maria; Trombetti, Marco

doi:10.22108/ijgt.2021.129515.1700

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	Infinite locally finite simple groups with many complemented subgroups
International Journal of Group Theory
مقاله 5، دوره 11، شماره 3، آذر 2022، صفحه 191-200 اصل مقاله (475.23 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2021.129515.1700
نویسندگان
Maria Ferrara¹؛ Marco Trombetti^* ²
¹Dipartimento di Matematica e Fisica, Universit degli Studi della Campania “Luigi Vanvitelli”, viale Lincoln 5, Caserta, Italy
²Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Universit degli Studi di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, Napoli, Italy
چکیده
We prove that the following families of (infinite) groups have complemented subgroup lattice‎: ‎alternating groups‎, ‎finitary symmetric groups‎, ‎Suzuki groups over an infinite locally finite field of characteristic $2$‎, ‎Ree groups over an infinite locally finite field of characteristic~$3$‎. ‎We also show that if the Sylow primary subgroups of a locally finite simple group $G$ have complemented subgroup lattice‎, ‎then this is also the case for $G$‎.
کلیدواژه‌ها
$K$-group‎؛ ‎complemented subgroup‎؛ ‎locally finite simple group

مراجع
[1] R. C. Alperin, PSL2 (Z) = Z2 ∗ Z3 , Amer. Math. Monthly, 100 (1993) 385–386. [2] R. Baer, Die Kompositionsreihe der Gruppe aller eineindeutigen Abbildungen einer unendlichen Menge auf sich, Stud. Math., 5 (1934) 15–17. [3] R. W. Carter, Simple groups of Lie type, Wiley, New York, 1972. [4] M. Costantini and G. Zacher, The finite simple groups have complemented subgroup lattices, Pacific J. Math., 213 (2004) 245–251. [5] M. Ferrara and M. Trombetti, A local study of group classes, Note Mat., 42 (2020) 1–20. [6] M. Ferrara and M. Trombetti, Infinite groups with many complemented subgroups, Beitr. Alg. Geom, to appear; doi:10.1007/s13366-021-00597-w. [7] J. Hall, Infinite alternating groups as finitary linear transformation groups, J. Algebra, 119 (1988) 337–359. [8] B. Hartley and G. Shute, Monomorphisms and direct limits of finite groups of Lie type, Quart. J. Math. Oxford (2), 35 (1984) 49–71. [9] O. H. Kegel and B. A. F. Wehrfritz, Locally finite groups, North-Holland, London, 1973. [10] V. M. Levchuk and Ya. N. Nuzhin, Structure of Ree groups, Algebra and Logic, 24 (1985) 16–26. [11] A. Yu. Ol’shanskij, Geometry of defining relations in groups, Kluwer Academy Publishers, Dordrecht, 1991. [12] E. Previato, Some families of simple groups whose lattices are complemented, Boll. U. M. I., 6 (1982) 1003–1014. [13] D. J. S. Robinson, Finiteness conditions and generalized soluble groups, Springer, Berlin, 1972. [14] D. J. S. Robinson, A course in the theory of groups, Springer, Berlin, 1995. [15] R. Schmidt, Subgroup lattices of groups, De Gruyter, Berlin, 1994. [16] M. Suzuki, On a class of doubly transitive groups, Ann. Math., 75 (1962) 105–145. [17] H. N. Ward, On Ree’s series of simple groups, Trans. Amer. Math. Soc., 121 (1966) 62–89. [18] B. A. F. Wehrfritz, Infinite linear groups, Springer, Berlin, 1973.
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Infinite locally finite simple groups with many complemented subgroups