Abstract
We establish the dependence of the derived length and p-length of a finite soluble group on its rank.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Huppert B., Endliche Gruppen. I, Springer-Verlag, Berlin, Heidelberg, and New York (1967).
Huppert B., “Normalteiler und maximale Untergruppen endlicher Gruppen,” Math. Z., Bd 60, 409–434 (1954).
Rose J., “Sufficient conditions for the existence of ordered Sylow towers in finite groups,” J. Algebra, 28, 116–126 (1974).
Zassenhaus H., “Beweis eines Zatzes uber diskrete Gruppen,” Abh. Math. Sem. Univ. Hamburg, Bd 12, 289–312 (1938).
Schmidt O. Yu., “Groups whose all subgroups are special,” Mat. Sb., 31, 366–372 (1924).
Golfand Yu. A., “On groups all subgroups of which are special,” Dokl. Akad. Nauk SSSR, 60, No. 8, 1313–1315 (1948).
Monakhov V. S., “The Schmidt subgroups, its existence, and some of their applications,” in: Proceedings of the Ukrainian Mathematical Congress-2001, Kiev, Ukraine, August 21–23, 2001. Section 1. Algebra and Number Theory. Inst. Mat. NAN Ukrainy, Kyiv, 2002, pp. 81–90.
Chunikhin S. A., “Sets of nonspecial subgroups and p-nilpotency of finite groups,” Dokl. Akad. Nauk SSSR, 118, No 4, 654–656 (1958).
Gaschutz W., Lectures on Subgroups of Sylow Type in Finite Soluble Groups, Australian National Univ., Canberra (1979) (Notes Pure Math; 11.)
Shemetkov L. A., Formations of Finite Groups [in Russian], Nauka, Moscow (1978).
Schmid P., “Every saturated formation is a local formation,” J. Algebra, 51, 144–148 (1978).
Mann A., “The derived length of p-groups,” J. Algebra, 224, 263–267 (2000).
Bloom D., “The subgroups of PSL(3, q) for odd q,” Trans. Amer. Math. Soc., 127, No. 1, 150–178 (1967).
Suprunenko D. A., Matrix Groups [Russian], Nauka, Moscow (1972).
Flannery D. L. and O’Brien E. A., “Linear groups of small degree over finite fields,” Intern. J. Algebra Comput., 15, No. 3, 467–502 (2005).
Dixon J. D., “The solvable length of a solvable linear groups,” Math. Z., Bd 12, 151–158 (1968).
Huppert B. and Blackburn N., Finite Groups. II, Springer-Verlag, Berlin, Heidelberg, and New York (1982).
Dixon J. D., The Structure of Linear Groups, Van Nostrand Reinhold Company, London etc. (1971).
Bryukhanova E. G., “Connection between the 2-length and the derived length of a Sylow 2-subgroup of a finite solvable group,” Math. Notes, 29, No. 2, 85–90 (1981).
Berkovich Y., “Solvable permutation groups of maximal derived length,” Algebra Colloq., 4, No. 2, 175–186 (1997).
Palfy P. P., “Bounds for linear groups of odd order,” Rend. Circ. Mat. Palermo. Ser. 2, 39, No. 23, 253–263 (1990).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text Copyright © 2011 Monakhov V. S. and Trofimuk A. A.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 5, pp. 1123–1137, September–October, 2011.
Rights and permissions
About this article
Cite this article
Monakhov, V.S., Trofimuk, A.A. On finite soluble groups of fixed rank. Sib Math J 52, 892–903 (2011). https://doi.org/10.1134/S0037446611050144
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446611050144