Geodesic
ON GENERALISED PRONORMAL SUBGROUPS OF FINITE GROUPS
Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 691-703

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For a formation $\mathfrak F$, a subgroup M of a finite group G is said to be $\mathfrak F$-pronormal in G if for each g ∈ G, there exists x ∈ 〈U,Ug〉$\mathfrak F$ such that Ux = Ug. Let f be a subgroup embedding functor such that f(G) contains the set of normal subgroups of G and is contained in the set of Sylow-permutable subgroups of G for every finite group G. Given such an f, let fT denote the class of finite groups in which f(G) is the set of subnormal subgroups of G; this is the class of all finite groups G in which to be in f(G) is a transitive relation in G. A subgroup M of a finite group G is said to be $\mathfrak F$-normal in G if G/CoreG(M) belongs to $\mathfrak F$. A subgroup U of a finite group G is called K-$\mathfrak F$-subnormal in G if either U = G or there exist subgroups U = U0 ≤ U1 ≤ . . . ≤ Un = G such that Ui–1 is either normal or $\mathfrak F$-normal in Ui, for i = 1,2, ..., n. We call a finite group G an $fT_{\mathfrak F}$-group if every K-$\mathfrak F$-subnormal subgroup of G is in f(G). In this paper, we analyse for certain formations $\mathfrak F$ the structure of $fT_{\mathfrak F}$-groups. We pay special attention to the $\mathfrak F$-pronormal subgroups in this analysis.
DOI : 10.1017/S0017089514000159
Mots-clés : 20D10, 20D35, 20F17 
BALLESTER-BOLINCHES, A.; BEIDLEMAN, J. C.; FELDMAN, A. D.; RAGLAND, M. F. ON GENERALISED PRONORMAL SUBGROUPS OF FINITE GROUPS. Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 691-703. doi: 10.1017/S0017089514000159
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