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The document examines some lattice theoretic properties in the subgroup lattices of symmetric groups. It proves that: 1) The lattice of subgroups L(Sn) is distributive and pseudo-complemented if and only if n ≤ 2. 2) L(Sn) satisfies the general disjointness condition, is supermodular, and semi-supermodular if and only if n ≤ 3. 3) Every atom in L(S4) and L(S5) is non-modular. Specifically, it proves every atom in L(S4) and L(S5) fails the modular law. 4) L(Sn) is supersolvable when n ≤ 3

Author

aye pyone

Language

EN