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that shows that the set of products of one of the two left cosets of one of the subgroups of order 2 (all of which are non-normal) with itself consists of
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In the definitions section, there is both -g H g = H and -g H g included in H but they are not equivalent in infinite groups.
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Example in which the set of products of two left cosets of a non-normal coset does not even equal a coset
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looks a bit like original research, but a very similar proof is given in Dummit & Foote 3ed, p81.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
503:, as expected; I suspect that the product set of two left cosets of a finite non-normal subgroup
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The StackExchange answer goes on to show how, if the operation were instead defined as (
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459:={(1 2),(1 3),(2 3)} and the products of elements of this coset with itself are
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I'm not sure about how useful it would be in the main article, but I found
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I'm trying to find something to support/refute the idea that
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