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Groups of order 2048 with three generators and three relationsKeywords: Schur multiplier , presentation , deficiency zero , finite $p$-group , lower exponent-$p$ central series Abstract: It is shown that there are exactly seventy-eight 3-generator 2-groups of order $2^{11}$ with trivial Schur multiplier. We then give 3-generator, 3-relation presentations for forty-eight of them proving that these groups have deficiency zero.
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