Question

Difference between subgroups and normal subgroup in fuzzy set

Answer 1

In abstract algebra, a normal subgroup is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup H of a group G is normal in G if and only if gH = Hg for all g in G. The definition of normal subgroup implies that the sets of left and right cosets coincide. In fact, a seemingly weaker condition that the sets of left and right cosets coincide also implies that the subgroup H of a group G is normal in G. Normal subgroups (and only normal subgroups) can be used to construct quotient groups from a given group.

Algebraic structure → Group theory

Group theory

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Subgroup Normal subgroup

Quotient group (Semi-)direct product

Group homomorphisms

kernel image direct sum

wreath product simple finite

infinite continuous multiplicative

additive cyclic abelian dihedral

nilpotent solvable

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