4

Part of 2013 Miklós Schweitzer

Problems(1)

An Abelian Group of size n

Source: Miklós Schweitzer 2013, P4

A

be an Abelian group with

n

elements. Prove that there are two subgroups in

\text{GL}(n,\Bbb{C})

, isomorphic to

S_n

, whose intersection is isomorphic to the automorphism group of

A

.
Proposed by Zoltán Halasi

abstract algebragroup theorysuperior algebrasuperior algebra unsolved