On the Subgroup Lattice of an Abelian Finite Group
نویسنده
چکیده
The aim of this paper is to give some connections between the structure of an abelian finite group and the structure of its subgroup lattice. Let (G, +) be an abelian group. Then the set L(G) of subgroups of G is a modular and complete lattice. Moreover, we suppose that G is finite of order n. If L n is the divisors lattice of n, then the following function is well defined: ord : L(G) −→ L n , ord(H) = |H|, for any H ∈ L(G), where by |H| we denote the order of the subgroup H. 2 Main results Proposition 1. The following conditions are equivalent: (i) G is a cyclic group. (ii) ord is an one-to-one function.
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