Abstract
We study the structure of the lattice Regtrϰ) of all regular transitive subgroup ϰ-functors. We describe all hereditary formations ϰ for which the width of Regtr(ϰ) is finite and does not exceed |π(ϰ)|, where fy(ϰ) is the set of all prime divisors of the orders of the groups in ϰ.
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References
Kourovka Notebook: Unsolved Problems of Group Theory, Sobolev Inst. Mat., Novosibirsk (2006).
Skiba A. N., Algebra of Formations [in Russian], Belarusskaya Nauka, Minsk (1997).
Kamornikov S. F. and Sel’kin V. M., Subgroup Functors and Classes of Finite Groups [in Russian], Belarusskaya Nauka, Minsk (2003).
Shemetkov L. A., Formations of Finite Groups [in Russian], Nauka, Moscow (1978).
Grätzer G., General Lattice Theory, Birkhäuser, Basel (1978).
Guo W., Skiba A. N., and Sham K. P., “Lattices of subgroup and subsystem functors,” Algebra and Logic, 45, No. 6, 403–414 (2006).
Baer R., “Classes of finite groups and their properties,” Illinois J. Math., 1, 115–187 (1957).
Vasil’ev A. F. and Kamornikov S. F., “On the functorial method for studying the lattices of subgroups of finite groups,” Siberian Math. J., 42, No. 1, 25–33 (2001).
Neumann P. M., “A note on formations of finite nilpotent groups,” Bull. London Math. Soc., 2, No. 1, 91 (1970).
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Original Russian Text Copyright © 2010 Kamornikov S. F.
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 5, pp. 1034-1040, September-October, 2010
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Kamornikov, S.F. On The Lattice of Regular Transitive Subgroup Functors. Sib Math J 51, 824–829 (2010). https://doi.org/10.1007/s11202-010-0083-7
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DOI: https://doi.org/10.1007/s11202-010-0083-7