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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
set-theory&algebra
abelian-group
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
set-theory&algebra
abelian-group
testbook-test-series
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
by
Dknights
117
views
set-theory&algebra
abelian-group
group-theory
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
by
GO Classes
194
views
goclasses_wq12
goclasses
set-theory&algebra
group-theory
abelian-group
1-mark
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
by
GO Classes
144
views
goclasses_wq12
goclasses
set-theory&algebra
group-theory
abelian-group
2-marks
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
by
GO Classes
208
views
goclasses_wq12
goclasses
set-theory&algebra
group-theory
abelian-group
multiple-selects
2-marks
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
nielit2016dec-scientistb-cs
discrete-mathematics
group-theory
abelian-group
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
nielit2017dec-scientistb
discrete-mathematics
group-theory
abelian-group
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
abelian-group
set-theory&algebra
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
isro2018
group-theory
set-theory&algebra
abelian-group
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_$_h
asked
in
Set Theory & Algebra
Jan 30, 2018
by
A_i_$_h
430
views
abelian-group
group-theory
2
votes
2
answers
12
GROUP
does it satisfy for every subset of R?
raviyogi
asked
in
Engineering Mathematics
Jan 25, 2018
by
raviyogi
363
views
group-theory
discrete-mathematics
set-theory&algebra
abelian-group
engineering-mathematics
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
abelian-group
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
by
Venkat Sai
119
views
abelian-group
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
abelian-group
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
by
Manu Thakur
2.6k
views
discrete-mathematics
group-theory
abelian-group
set-theory&algebra
1
vote
0
answers
17
testbook test series
rohit vishkarma
asked
in
Set Theory & Algebra
Nov 2, 2017
by
rohit vishkarma
218
views
abelian-group
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
discrete-mathematics
group-theory
abelian-group
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
set-theory&algebra
group-theory
abelian-group
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Recent questions tagged abelian-group
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