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An Abelian Group of size n

Source: Miklós Schweitzer 2013, P4

June 28, 2014
abstract algebragroup theorysuperior algebrasuperior algebra unsolved

Problem Statement

Let AA be an Abelian group with nn elements. Prove that there are two subgroups in GL(n,C)\text{GL}(n,\Bbb{C}), isomorphic to SnS_n, whose intersection is isomorphic to the automorphism group of AA.
Proposed by Zoltán Halasi
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