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Lets $G$ is finite abelian group (such that for any $x\in G$ $x+x=0$, i.e. $G=\mathbb{Z}_{2}^{\oplus k}$ for some $k\in\mathbb{N}$) and $(\cdot,\cdot):G\times G\to \mathbb{Z}_{2}$ is symmetrical bilinear form.

Know that: $$(a, m)=0,$$ $$(a, p)=1,$$ $$(b, m)=1,$$ $$(b, p)=0.$$

Is it true that $$(a, b) = 1?$$

Thanks.

  • 1
    The "i.e." is incorrect. Nothing before that excludes the possibility that $G$ is infinite.2012-03-01
  • 0
    @joriki: Lets $G$ is finite2012-03-01

2 Answers 2