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We study the quotient of the mapping class group    Mod  g  n    of a surface of genus   g   with   n   punctures, by the subgroupMod  g  n    [  p  ]generated by the   p  th powers of Dehn twists.  Our first main result is thatMod  g  1   /   Mod  g  1    [  p  ]contains an infinite normal subgroup of infinite index, and in particular is not commensurable to a higher rank lattice, for all but finitely many explicit values of   p  . Next, we prove thatMod  g  0   /   Mod  g  0    [  p  ]contains a Kähler subgroup of finite index, for every    p  ⩾  2    coprime with six. Finally, we observe that the existence of finite‐index subgroups of    Mod  g  0    with infinite abelianization is equivalent to the analogous problem forMod  g  0   /   Mod  g  0    [  p  ]    .

Quotients of the mapping class group by power subgroups