Abstract. The frame of a group is the poset of conjugacy classes of all its proper subgroups. In this paper we will prove that a finite group is solvable if and only if every collection of maximal elements of its frame has a well-defined meet and the poset consisting of all such meets (including the meet of the empty set) is a modular lattice.
A characterization of solvability for finite groups in terms of their frame / F. Fumagalli, G. Malle. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 322:(2009), pp. 1919-1945. [10.1016/j.jalgebra.2009.06.005]
A characterization of solvability for finite groups in terms of their frame
F. Fumagalli
;
2009
Abstract
Abstract. The frame of a group is the poset of conjugacy classes of all its proper subgroups. In this paper we will prove that a finite group is solvable if and only if every collection of maximal elements of its frame has a well-defined meet and the poset consisting of all such meets (including the meet of the empty set) is a modular lattice.
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