noun, plural complicities.
the state of being an accomplice; partnership or involvement in wrongdoing: complicity in a crime.

1650–60; < Late Latin complic-, stem of complex complice + -ity

complicitous, adjective
noncomplicity, noun, plural noncomplicities.

collusion, intrigue, implication, connivance. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
complicity (kəmˈplɪsɪtɪ)
n , pl -ties
1.  the fact or condition of being an accomplice, esp in a criminal act
2.  a less common word for complexity

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

1650s, from Fr. complicité, from M.Fr., from O.Fr. complice "accomplice," from L.L. complicem, acc. of complex "partner, confederate," from L. complicare "to fold together" (see complicate).
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Then, you have the complicity of those easily fooled, who should know better.
He must simultaneously suggest offensiveness and disarm it, with an invitation
  to hip complicity.
Leaders in the region, lulled into complicity by the ease with which they had
  subdued their populations to date, didn't listen.
Up to now, the bishops have not admitted any personal complicity.
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