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Challenge! Can you find number of non-isomorphic cyclic groups of order n?

How to find number of non-isomorphic abelian groups of order n? | Tamil ...

An Euclidean ring (domain)

 Qn 1 :

 An Euclidean ring must possess ................ element.

a) Unity
 b) Unit

 Qn 2 :

An Euclidean ring must possess ................
a) Unity
 b) Unit .

Answer by Prof. Suresh:

Qn 1 - b 

Qn 2 - a
unity = unit element = multiplicative identity.

Note:
Unit means multiplicative inverse.

Unity element - meaningless.
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MODERN ALGEBRA - GROUP THEORY Notes

 

Algebra - Group Theory MCQ Q&A

Algebra - Group Theory Q&A

Useful for B.Sc / M.Sc Maths | TRB | CSIR NET/SET | TNPSC

1) Cycle of length two is called ...... 

 A) perfect cycle
B) Transposition
C) Even permutation


2) A group generated by a single element is called __________


3) S_n is non-abelian when ......... 

A) n ≥ 2
B) n ≤ 2
C ) n ≤ 3
D) n ≥ 3


4) Identity permutation is a ___________ permutation.
A) Odd
B) Even
C) Both odd and even.

5) The general linear group of degree n is,

 A) A set of  n×n singular matrices

 B) A set of  n×n invertible matrices

 C) The set of  all n×n matrices

 D) The set of  all n×n matrices with determinant 1.

Answers:
1 - B

2 - cyclic group

3 - D

4 - B

5 - B

3 in 1 - OR / Analysis / Algebra

 Prof.Suresh CSIR NET & SET:

If there are n jobs and n workers there are n! (total) possible assignments.

No of bijective functions from a set A of n elements to a set B of n elements is ...... n!

Number of elements in Permutation group Sn ...... n!

இந்த மூன்றையும் connect பண்ணி யோசிங்க.

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Algebra - Group Theory Q&A in Tamil | TN TRB PG | CSIR NET | SET

Algebra - Group Theory Q&A | TN TRB PG | CSIR NET | SET.

Group

Definition : A non-empty set G is said to form a group if  in G there is defined a binary operation, called the product and denoted by (·) such that

1.    a, b ∈ G ⇒ a · b ∈ G (Closure axiom)

2.    a, b, c ∈ G ⇒ a · (b · c) = (a · b) · c (Associative axiom)

3.    There exists an element e ∈ G such that a · e = e · a = a, ∀ a ∈ G (Existence of  identity)

4.     ∀ a ∈ G there exists an element a⁻¹ ∈ G such that a·a⁻¹ = a⁻¹ ·a = e (Existence of inverse).

(Z, +) is an infinite abelian group.

Also (Q, +), (R , +), (C, +) are infinite abelian groups.

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How to calculate product of permutations | TRB PG Q&A | Algebra

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Algebra - Cyclic Group in Tamil for TRB PG / Poly , CSIR NET/SET Maths

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Number Theory: Chinese Remainder Theorem & Solved Problem in Tamil | P...

Modern Algebra

The order of 2 in the group (Z_8 , +_8) is .....