Groups in 2016

Algebra Level 4

Let \((G,\circ)\) be a finite abelian group of order \(n\), say \(G=\{a_i\}_{i=1}^{i=n}\), where \(n\) is a positive integer. Also, let \(x=a_1\circ a_2\circ\cdots\circ a_{n-1}\circ a_n\).

What is the value of \(x^{2016}?\)

Details and Assumptions:

  • \(e_G\) denotes the identity element of the group \((G,\circ)\).
  • \(x^n=\underbrace{x\circ x\circ\cdots\circ x\circ x}_{n\textrm{ times}}\).

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