Use cosets in a sentence - Example Sentences for cosets
The image (mathematics) of this map is the orbit of 'x' and the coimage is the set of all left cosets of 'Gx'.
"When θ is the trivial character of 'H', the induced character obtained is known as the 'permutation character' of 'G' (on the cosets of 'H')."
This is because if 'C' is the identity component, 'a*C' is the component of 'G' (the group) containing a. In fact, the collection of all left cosets (or right cosets) of 'C' in 'G' is equal to the collection of all components of 'G'.
For example, the index of 'H' in 'G' may be countable set or Uncountable set, depending on whether 'H' has a countable number of cosets in 'G'.
In the study of discrete space subgroups of Lie groups, the quotient space of cosets is often a candidate for more subtle 'compactification' to preserve structure at a richer level than just topological.
Its basic form concerns the way a character (or module) induced from a subgroup 'H' of a finite group 'G' behaves on restriction back to a (possibly different) subgroup 'K' of 'G', and makes use of the decomposition of 'G' into ('H','K')-double cosets.
If 'H' has an infinite number of cosets in 'G', then the index of 'H' in 'G' is said to be infinite.
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The word cosets
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