what are cosets and where it is used practically
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hiiii mate here your answer ✔️ ✔️
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In mathematics, if G is a group, and H is a subgroup of G, and g is an element of G, then
gH = { gh : h an element of H } is the left coset of H in G with respect to g, andHg = { hg : h an element of H } is the right coset of H in G with respect to g.
Only when H is normal will the set of right cosets and the set of left cosets of Hcoincide, which is one definition of normality of a subgroup. Although derived from a subgroup, cosets are not usually themselves subgroups of G, only subsets.
A coset is a left or right coset of somesubgroup in G. Since Hg = g ( g−1Hg ), the right coset Hg (of H with respect to g) and the left coset g ( g−1Hg ) (of the conjugate subgroup g−1Hg ) are the same. Hence it is not meaningful to speak of a coset as being left or right unless one first specifies the underlying subgroup. In other words: a right coset of one subgroup equals a left coset of a different (conjugate) subgroup. If the left cosets and right cosets are the same, then His a normal subgroup and the cosets form a group called the quotient or factor group.
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______________________________
In mathematics, if G is a group, and H is a subgroup of G, and g is an element of G, then
gH = { gh : h an element of H } is the left coset of H in G with respect to g, andHg = { hg : h an element of H } is the right coset of H in G with respect to g.
Only when H is normal will the set of right cosets and the set of left cosets of Hcoincide, which is one definition of normality of a subgroup. Although derived from a subgroup, cosets are not usually themselves subgroups of G, only subsets.
A coset is a left or right coset of somesubgroup in G. Since Hg = g ( g−1Hg ), the right coset Hg (of H with respect to g) and the left coset g ( g−1Hg ) (of the conjugate subgroup g−1Hg ) are the same. Hence it is not meaningful to speak of a coset as being left or right unless one first specifies the underlying subgroup. In other words: a right coset of one subgroup equals a left coset of a different (conjugate) subgroup. If the left cosets and right cosets are the same, then His a normal subgroup and the cosets form a group called the quotient or factor group.
______________________________
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karthiji:
its too theoritical. i want some few example that whats are its applications
will you
what application
applications of cosets
its my project
no no his answer in my science noted
anyway thankyou
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