ON DECOMPOSABILITY OF FINITE GROUPS
Copyright policy )ON DECOMPOSABILITY OF FINITE GROUPS
Let \(G\) be a finite group and \(N_G\) be the set of proper normal subgroups of \(G\). An element \(N\) of \(N_G\) is said to be \(n\)-decomposable if \(N\) is a union of \(n\) conjugacy classes of \(G\). Here we denote \(n\) by \(ncc(N)\). Suppose \(K_G=\{ncc(N)\mid N\triangleleft G\}\), \(K_G\) is a non-empty subset of positive integers. The reviewer [A class of special minimal normal subgroups, J. Southwest Teachers Coll. 9, 9-13 (1984)], discussed those finite groups \(G\) in which \(K_G\) contains \(2\). In this paper, the author continues his former works and characterizes the finite groups \(G\) with \(K_G=\{1,3,4\}\). A GAP program is used in the paper.
\(n\)-decomposable subgroups, unions of conjugacy classes, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Series and lattices of subgroups, Arithmetic and combinatorial problems involving abstract finite groups, finite groups, Conjugacy classes for groups
\(n\)-decomposable subgroups, unions of conjugacy classes, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Series and lattices of subgroups, Arithmetic and combinatorial problems involving abstract finite groups, finite groups, Conjugacy classes for groups
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