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Let D denote the (n-1)-dimensional simplex. Let Y be a random 2-dimensionalsubcomplex of D obtained by starting with the full 1-skeleton of D and thenadding each 2-simplex independently with probability p. For a fixed c>0 it isshown that if p=\frac{(6+7c) \log n}{n} then a.a.s. the fundamental group\pi(Y) does not have a nontrivial quotient of order at most n^c.

Bounded quotients of the fundamental group of a random 2-complex