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On an embedding property of generalized Carter subgroups

1969
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Pacific Journal of Mathematics
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If if and J^"~are saturated formations, ί §Γ is strongly contained in &~ (written gf « jr) if : (1.1) For any solvable group G with if -subgroup E, andj^~subgroup F, some conjugate of E is contained in F. This paper is concerned with the problem: (1.2) Given g% what saturated formations J^~satisfy g 7 « J^"? The object of this paper is to prove two theorems. The first, Theorem 5.3, shows that if J7" is a nonempty formation, and ξ?={G\GIF(G)ejT} 9 (F(G) is the Fitting subgroup of G), then any

doi:10.2140/pjm.1969.29.491
fatcat:fij24smkbvdldfkr4uos2qbzty