Abstract
Intersections of given maximal subgroups of finite groups are studied. General properties of the generalized Frattini subgroup are established with the help of functorial methods.
Similar content being viewed by others
References
G. Frattini, “Intorno alla Generasione dei Gruppi di Operazioni,” Atti Acad. Lincei., 1, 281 (1885).
L. A. Shemetkov, Formations of Finite Groups (Nauka, Moscow, 1978) [in Russian].
M. V. Sel’kin, Maximal Subgroups in the Theory of Classes of Finite Groups (Belaruskaya Navuka, Minsk, 1997) [in Russian].
J. G. Thompson, “Normal p-Complements for Finite Groups,” J. Algebra 1, 43 (1964).
O. A. Shpyrko, “The Derived π-Length of a Finite π-Solvable Group,” Tavrich. Vestnik Inform. Matem., No 1, 49 (2005).
P. Hall and G. Higman, “On the p-Length of p-Soluble Groups and Reduction Theorems for Burnside’s Problem,” Proc. London Math. Soc. 3, 1 (1956).
Author information
Authors and Affiliations
Additional information
Original Russian Text © R.V. Borodich and O.A. Shpyrko, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 5, pp. 3–6.
About this article
Cite this article
Borodich, R.V., Shpyrko, O.A. Intersection of functorial subgroups in finite groups. Moscow Univ. Math. Bull. 66, 185–188 (2011). https://doi.org/10.3103/S0027132211050019
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0027132211050019