Find all abelian groups of order 2700 b rohant sodhur

Q: Write the Caley table of all abelian groups of order 8

A: We have to write cayley table of abelian group of order 8.

Q: Write under isomorphism all the abelian groups of order 8 and their respective subgroups.

A: To find all the abelian groups of order 8, we can use the fundamental theorem of finitely generated…

Q: Find all the non-isomorphic abelian groups of order 32.

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Q: Find all abelian groups (upto isomorphism) of order 3375.

A: We have to find the all abelian groups (upto isomorphism) of order 3375.

Q: give an example of a finite, non-cyclic abelian group containing a container of order 5

A: Take the abelian group G=Z5×Z5 of order 25 whose every element (except identity) is of order 5 and…

Q: Give an example of a non-Abelian group that has exactly threeelementsof finite order.

A: Let G=Z3⊕Z be an additive group where e=0,0. Let x∈G then it can be observed that x=a,b where a∈Z3,…

Q: Find any case in which the number of subgroups with an order of 3 can be exactly 4 in the Abelian…

A: Let G be an abelian group of order 108 Find the number of subgroups of order 3. Prove that, in any…

Q: Find the non-isomorphic abelian groups of  order 360.

A: We have to find the non -isomorphic abelian group of order 360.

Q: How many nonisomorphic abelian groups of order 80000 are there?

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Q: Find the number of non-isomorphic abelian groups of order 160. How many of these groups will be…

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Q: Show that a group of order pn, where p is prime, is solvable.

A: Let G be a group of order p^n, where p is a prime number.   We will prove by induction on n that G…

Q: Show that a group G of order pq for  distinct primes p and q is solvable.

A: Introduction: A solvable group is a group having a normal series such that each normal factor is…

Q: Prove that a cyclic group with even number of elements contains ex- actly one element of order 2.

A: The solution is given as

Q: Find all abelian groups (upto isomorphism)  of order 67

A: We have to find all abelian groups (upto isomorphism) of order 675.

Q: Find all abelian groups upto isomorphism  of order 4 and 6.

A: We have to find the all abelian groups upto isomorphism of order 4 and 6.

Q: Let G = Z4 x Z6. Compute the factor groups G/((2, 3)) and G/((3, 3)). (In each case, write the…

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Q: Write the Caley table of all abelian groups of order 8 Please be legible.

A: Introduction: A group is a set of elements closed under an associative operation that includes an…

Q: Determine the class equation for non-Abelian groups of orders 39and 55.

A: We have to determine the class equation for non-Abelian groups of orders 39 and 55.

Q: List six examples of non-Abelian groups of order 24.

A: The Oder is 24

Q: Give an example of two non-homomorphic finite abelian groups that have the same number of elements…

A: We need to find an example of two non holomorphic finite abelian groups which have the same number…

Q: Up to isomorphism, list all abelian groups of order 1350.

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Q: Find two p-groups of order 4 that are not isomorphic.

A: Consider the groups ℤ4  and  ℤ2⊕ℤ2. Clearly, both of the above groups are p-groups of order 4.

Q: List all abelian groups (up to isomorphism) of order 600

A: To List all abelian groups (up to isomorphism) of order 600

Q: Show that a group of order 12 cannot have nine elements of order 2.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Write the Caley table of all non-abelian groups of order 8.

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