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Recent questions tagged abelian-group

1 vote

2 answers

1

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 3 days ago

by Sahil_Lather

37 views

1 vote

2 answers

2

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 3 days ago

by Sahil_Lather

40 views

0 votes

0 answers

3

#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

117 views

4 votes

1 answer

4

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 3
In a group $\text{G},$ every element other than the identity element has order $2$ then $\mathrm{G}$ is? Abelian group Cyclic group Non-abelian group Non-cyclic group

GO Classes asked in Set Theory & Algebra May 29, 2022

194 views

3 votes

1 answer

5

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 7
Let $R$ be the set of all real numbers. Let $S=R \backslash\{-1\}$ and define a binary operation on $S$ by $a \ast b=a+b+a b$. Which of the following is true? $(\mathrm{S}, \ast)$ is a not a group. ... not abelian. $(\mathrm{S}, \ast)$ is a cyclic group. $(\mathrm{S}, \ast)$ is an abelian group but not cyclic.

GO Classes asked in Set Theory & Algebra May 29, 2022

144 views

1 vote

1 answer

6

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 15
Let $G$ be a group under binary operation *. Let $g \in G$. We define $<g>$ as follows : $\langle g\rangle=\left\{g^{n} \mid n \in \mathbb{Z}\right\}$ ... $G$. $<g>$ is abelian. If $H \leq G$ and $g \in H$, then $< g>\leq H$.

GO Classes asked in Set Theory & Algebra May 29, 2022

208 views

2 votes

1 answer

7

NIELIT 2016 DEC Scientist B (CS) - Section B: 28
Which one of the following is NOT necessarily a property of a Group? Commutativity Associativity Existence of inverse for every element Existence of identity

Lakshman Patel RJIT asked in Set Theory & Algebra Mar 31, 2020

by Lakshman Patel RJIT

430 views

3 votes

5 answers

8

NIELIT 2017 DEC Scientist B - Section B: 48
On a set $A = \{a,b,c,d\}$ a binary operation $*$ ... The relation is Commutative but not associative Neither commutative nor associative Both commutative and associative Associative but not commutative

Lakshman Patel RJIT asked in Set Theory & Algebra Mar 30, 2020

by Lakshman Patel RJIT

1.3k views

0 votes

0 answers

9

Abelian Group
Prove with examples:- The set of all rational numbers except 0 are abelian group under multiplication. The set of all real numbers except 0 are closed under abelian group under multiplication.

Shamim Ahmed asked in Set Theory & Algebra Jan 8, 2019

by Shamim Ahmed

204 views

8 votes

3 answers

10

ISRO2018-17
$(\text{G}, \ast )$ is an abelian group. Then $x= x^{-1}$ for any $x$ belonging to $\text{G}$ $x=x^{2}$ for any $x$ belonging to $\text{G}$ $\left( x \ast y \right )^{2}= x^{2} \ast y^{2}$ , for any $x, y$ belonging to $\text{G}$ $\text{G}$ is of finite order

Arjun asked in Set Theory & Algebra Apr 22, 2018

by Arjun

3.3k views

2 votes

1 answer

11

non abelian
Let G be a non abelian group, order of G can be 24 44 54 34

A_i_$_h asked in Set Theory & Algebra Jan 30, 2018

430 views

2 votes

2 answers

12

GROUP
does it satisfy for every subset of R?

raviyogi asked in Engineering Mathematics Jan 25, 2018

363 views

0 votes

0 answers

13

Non Abelian Group
Let G be a non-abelian group, order of G can be ? (A) 24 (B) 44 (C) 54 (D) 34

ankitgupta.1729 asked in Set Theory & Algebra Dec 6, 2017

by ankitgupta.1729

670 views

0 votes

0 answers

14

PLEASE HELP
i find many theorems ON ABELIAN GROUPS CAN SOMEONE SUGGEST ME ONE PLACE WHERE I GET THEOREMS ON ABELIAN GROUPS

Venkat Sai asked in Set Theory & Algebra Dec 3, 2017

119 views

0 votes

0 answers

15

Abeian group , need proof .
{ - 3 n : n ε Z } IS an abelian group under A

hem chandra joshi asked in Set Theory & Algebra Nov 6, 2017

by hem chandra joshi

789 views

3 votes

2 answers

16

Maths: Group Theory
Que: Which one of the following is not true? a) In a group (G,*), if a*a = a, then a=e, where e is an identity element. b) In a group (G,*), if x-1 = x, ∀x ∈ G, then G is an Abelian group. c) In a group (G,*), if (a*b)2 = (a2*b2) then G is an Abelian group. ... (G,*), if (a*b)n = (an*bn) then G is an Abelian group, where n={2, 3, 4, ......} PS: c) and d) seem correct to me.

Manu Thakur asked in Set Theory & Algebra Nov 5, 2017

2.6k views

1 vote

0 answers

17

testbook test series

rohit vishkarma asked in Set Theory & Algebra Nov 2, 2017

by rohit vishkarma

218 views

0 votes

0 answers

18

[Discrete maths ] Group theory
Let G be abelian, H and K subgroups of G with orders n, m. Then G has subgroup of order lcm(n,m) I have gone through prrof here:- https://math.stackexchange.com/questions/465742/let-g-be-abelian-h-and-k-subgroups-of-orders ... this assertion true. there are some existing examples where n divides G but there is no subgroup with that order.Please clear with explanation.

rahul sharma 5 asked in Mathematical Logic Jun 13, 2017

by rahul sharma 5

532 views

0 votes

1 answer

19

Abelian Group
Question IF ( G, * ) is an abelian group then discuss correctness of each of the options ... a) a = a-1 for all a $\epsilon$ G b) a2 = a for all a $\epsilon$ G c) (a*b)2 = a2 * b2 for all a,b $\epsilon$ G d) G is finite ... a = a*b // cancelling a using left cancellation law and b using right cancellation law Therefore G is abelian group Given statement is correct D) PLEASE HELP ME ..

pC asked in Set Theory & Algebra Jun 27, 2016

by pC

3.3k views

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