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Recent questions tagged abelian-group

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UGC NET CSE | June 2008 | Part 2 | Question: 4
The set of positive integers under the operation of ordinary multiplication is : not a monoid not a group a group an Abelian group

admin asked in Others Jan 6

by admin

213 views

1 vote

1 answer

2

GO Classes 2023 | IIITH Mock Test 1 | Question: 5
$(\text{Q}, \ast)$ is an algebraic structure where $\text{Q}$ represents rational numbers and $\ast$ denotes multiplication. Which one of the following statements is true? $\text{Q}$ is an abelian group. $\text{Q}$ is a group but not abelian. $\text{Q}$ is a semigroup but not a monoid. $\text{Q}$ is monoid but not group.

GO Classes asked in Set Theory & Algebra Mar 26, 2023

530 views

1 vote

2 answers

3

Testbook set theory question for abelian group and generators
Given: Statement A: All cyclic groups are an abelian group. Statement B: The order of the cyclic group is the same as the order of its generator. 1 A and B are false 2 A is true, B is false 3 B is true, A is false 4 A and B both are true

Sahil_Lather asked in Set Theory & Algebra Jan 27, 2023

by Sahil_Lather

497 views

1 vote

2 answers

4

Testbook group theory question
Let G be a group of order 49. Then G is abelian G is cyclic G is non-abelian Centre of G has order 7

Sahil_Lather asked in Set Theory & Algebra Jan 27, 2023

by Sahil_Lather

495 views

0 votes

0 answers

5

#Unacademy
**Every group of prime order is always an abelian group on this fact please explain how can a 2 element group be an abelian group, please give an example

Dknights asked in Set Theory & Algebra Nov 4, 2022

350 views

3 votes

1 answer

6

GO Classes Test Series 2024 | Discrete Mathematics | Test 3 | Question: 3
$(\text{Q}, \ast)$ is an algebraic structure where $\text{Q}$ represents rational numbers and $\ast$ denotes multiplication. Which one of the following statements is true? $\text{Q}$ is an abelian group. $\text{Q}$ is a group but not abelian. $\text{Q}$ is a semigroup but not a monoid. $\text{Q}$ is monoid but not group.

GO Classes asked in Set Theory & Algebra Apr 27, 2022

484 views

4 votes

1 answer

7

GO Classes Test Series 2024 | Discrete Mathematics | Test 3 | Question: 15
Let $\text{G}$ be a group under binary operation $\ast .$ Let $g \in \text{G}.$ We define $\langle g \rangle$ as follows : $\langle g \rangle = \{g^{n} \mid n \in \mathbb{Z}\}.$ ... abelian. If $\text{H} \leq \text{G}$ and $g \in \text{H},$ then $ \langle g \rangle \leq \text{H}.$

GO Classes asked in Set Theory & Algebra Apr 27, 2022

429 views

3 votes

1 answer

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GO Classes Test Series 2024 | Discrete Mathematics | Test 3 | Question: 19
Which of the following are abelian group $\forall x, y \in$ integer? $x \ast y = x + y$ $x \ast y = \max (x, y)$ $x \ast y = x × y$ $x \ast y = x^{2} + y^{2}$

GO Classes asked in Set Theory & Algebra Apr 27, 2022

355 views

4 votes

1 answer

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GO Classes Test Series 2024 | Discrete Mathematics | Test 3 | Question: 20
Let $\text{R}$ be the set of all real numbers. Let $\text{S} = \text{R}\setminus \{-1\}$ and define a binary operation on $S$ by $a \ast b = a + b + ab.$ Which of the following is true? $(\text{R},\ast)$ is an ... $(\text{R},\ast),(\text{S},\ast)$ are abelian groups.

GO Classes asked in Set Theory & Algebra Apr 27, 2022

367 views

2 votes

1 answer

10

GO Classes Test Series 2024 | Discrete Mathematics | Test 3 | Question: 21
In a group $\text{G},$ every element other than the identity element has order $2$ then $\text{G}$ is? Abelian group Cyclic group Non-abelian group Non-cyclic group

GO Classes asked in Set Theory & Algebra Apr 27, 2022

422 views

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Recent questions tagged abelian-group