Show that set {1,2,3,4,5,6} is finite grp of order 6 under multiplication modulo 7 as composition

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Prove that set of natural no’s is a semi group but not a monoid under addition of natural numbers
   • Prove that set of natural no’s is a semi g...  

Show that set of all non-zero rational no’s is an abelian grp under multiplication of rational no’s
   • Show that set of all non-zero rational no’...  

Prove that the set of all even integers is an infinite abelian group under addition of integers
   • Prove that the set of all even integers is...  

Show that set of all positive rational numbers forms abelian grp under operation * (a*b = ab /3)
   • Show that set of all positive rational num...  

Show that set Q+ of all +ve rational numbers forms abelian group under operation * (a*b = ab/2)
   • Show that set Q+ of all +ve rational numbe...  

Prove :set of all non-zero complex no’s is infinite abelian grp under multiplication of complex no’s
   • Prove :set of all non-zero complex no’s is...  

Show that G = { a + √3b : a,b ∈ Q } is an abelian group under addition of real numbers.
   • Show that G = { a + √3b : a,b ∈ Q } is an ...  

Show that set {0,1,2,3,4,5,6} is finite group of order 7 under addition modulo 7 as composition
   • Show that set {0,1,2,3,4,5,6} is finite gr...  

Show that set {1,2,3,4,5,6} is finite grp of order 6 under multiplication modulo 7 as composition
   • Show that set {1,2,3,4,5,6} is finite  grp...  

Properties of group( Identity element in group is unique) bsc maths
   • Properties of group( Identity element in g...  

Inverse of each element of group is unique (bsc maths)
   • Inverse of each element of group is unique...  

Let (G,*) be a group.Then cancellation law holds in Group
   • Let (G,*) be a group.Then cancellation law...  

Prove set G of cube roots of unity is abelian group of order 3 under multiplication of complex no’s
   • Prove set G of cube roots of unity is abel...  

Prove that a group G is abelian if and only if (ab)^2 = a^2 b^2 for all a,b ∈ G.
   • Prove that a group G is abelian if and onl...  

Question on product of permutations in group theory. Compute p^-1qp (bsc maths)
   • Question on product of permutations in gro...  

Product of two disjoint cycles is commutative (group theory) bsc maths
   • Product of two disjoint cycles is commutat...  

Express the permutation as a product of disjoint cycles and find whether it is odd or even
   • Express the permutation as a product of d...  

Express the permutation p as a product of disjoint cycles, and find whether it is even or odd.
   • Express the permutation p as a product of ...  

Let H be a subgroup of group G. Then the identity element of H is same as the identity element of G.
   • Let H be a subgroup of group G. Then the i...  

A non-empty subset H of group G is a subgroup of G only if ab ∈ H ∀ a,b ∈ H & a^-1 ∀ a ∈ H theorem
   • A non-empty subset H of group G is a subgr...  

A non-empty subset H of a group G Is a subgroup of G if and only if ab inverse ∈ H
   • A non-empty subset H of a group G Is a sub...  

A non-empty finite subset H of a group G is a subgroup of G if and only if a.b ∈ H ∀ a, b ∈ H
   • A non-empty finite subset H of a group G i...  

Intersection of two subgroups of a group G is a subgroup of G (group theory bsc maths)
   • Intersection of two subgroups of a group G...  

The union of two subgroups of group G is a subgroup of G if and only if one is contained in other
   • The union of two subgroups of group G is a...  

HK is a subgroup of G if and only if HK = KH(product theorem) product of two subgroups
   • HK is a subgroup of G if and only if HK = ...  

Find the index of subgroup H={1,-1} in group G={1,-1,I,-I} under multiplication of complex numbers
   • Find the index of subgroup H={1,-1} in gro...  

Centre of a group. The centre of a group G is a subgroup of G.
   • Centre of a group.The centre of a group G ...  

Find the order of each element of the group {1,2,3,4} under multiplication modulo 5
   • Find the order of each element of the grou...  

Find the order of each element of the group {0,1,2,3,4,5} under addition modulo 6
   • Find the order of each element of the grou...  

Cyclic group.Prove that the order of a cyclic group is equal to the order of its generator .
   • Cyclic group.Prove that the order of a cyc...  

Every group of prime order is cyclic (group theory )
   • Every group of prime order is cyclic (grou...  

If a is a generator of a cyclic group G, then it’s inverse is also a generator.
   • If a is a generator of a cyclic group G, t...  

Every subgroup of a cyclic group is cyclic. Bsc maths group theory
   • Every subgroup of a cyclic group is cyclic...  

Prove that set {1,2,3,4,5,6} forms a cyclic group under multiplication modulo 7 find the generators
   • Prove that set {1,2,3,4,5,6} forms a cycli...