## Complete Sets of Orthogonal F-squares |

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0lll 2n-l)2 effects ABCD abelian group analysis of variance aoav binary operation closed under addition closed under multiplication complete set confounded with columns construct the complete contrasts of effects cyclic latin square decomposition degree of freedom denote effects AC effects unconfounded elements under addition factorial 2n factorial main effect factorial treatment design Figure II.l finite field freedom effects group G group of sn Hence interaction isomorphic k x k latin square l0ll LATIN SQUARE NUMBER let treatments ll0l lll0 llll multiplicative inverse one-to-one correspondence order sn orthogonal F-squares orthogonal F(A orthogonal F(A*,A orthogonal latin squares Proof prove Q.E.D. Theorem Q(oav Raghavarao rows and columns s2n factorial Seiden l970 set of orthogonal set of sn-l single degree sn elements sn-l effects unconfounded square of order subfield subgroup Sylow Theorem Theorem III.2 three effects treatment combinations unconfounded with rows