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In the example above, the identity and the rotations constitute a subgroup R = {id, r1, r2, r3}, highlighted in red in the group table above: any two rotations composed are still a rotation, and a rotation can be undone by (i.e. is inverse to) the complementary rotations 270 for 90, 180 for 180, and 90 for 270 (note that rotation in the opposite direction is not defined). The subgroup test is a necessary and sufficient condition for a subset H of a group G to be a subgroup: it is sufficient to check that g1h H for all elements g, h H. Knowing the subgroups is important in understanding the group as a whole.d["]

What essential condition must be met for a subset of a group to be a subgroup?
Answer: The subgroup test
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The content including match outcomes is choreographed and the combative actions and reactions are executed in special manners designed to both protect from, yet simulate, pain. These facts were once kept highly secret, but they are now openly declared as the truth. By and large, the true nature of the content is ignored by the performing promotion in official media in order to sustain and promote the willing suspension of disbelief for the audience by maintaining an aura of verisimilitude. Fan communications by individual wrestlers and promotions through outside media (i.e., interviews) will often directly acknowledge the fictional nature of the spectacle.

How are the actions conducted?
Answer: the combative actions and reactions are executed in special manners designed to both protect from, yet simulate, pain
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Sessions for West's sixth solo effort begin to take shape in early 2013 in his own personal loft's living room at a Paris hotel. Determined to "undermine the commercial", he once again brought together close collaborators and attempted to incorporate Chicago drill, dancehall, acid house, and industrial music. Primarily inspired by architecture, West's perfectionist tendencies led him to contact producer Rick Rubin fifteen days shy of its due date to strip down the record's sound in favor of a more minimalist approach. Initial promotion of his sixth album included worldwide video projections of the album's music and live television performances. Yeezus, West's sixth album, was released June 18, 2013 to rave reviews from critics. It became the rapper's sixth consecutive number one debut, but also marked his lowest solo opening week sales. Def Jam issued "Black Skinhead" to radio in July 2013 as the album's lead single. On September 6, 2013, Kanye West announced he would be headlining his first solo tour in five years, to support Yeezus, with fellow American rapper Kendrick Lamar accompanying him along the way.

What artist did Kanye go on tour with while promoting album number six?
Answer:
Kendrick Lamar