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Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
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Recent questions tagged groups
0
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1
answer
1
ISI2018MMA15
Let $G$ be a finite group of even order. Then which of the following statements is correct? The number of elements of order $2$ in $G$ is even The number of elements of order $2$ in $G$ is odd $G$ has no subgroup of order $2$ None of the above.
asked
May 11
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
41.6k
points)

55
views
isi2018mma
engineeringmathematics
discretemathematics
settheory&algebra
groups
+1
vote
1
answer
2
ISI2019MMA19
Let $G =\{a_1,a_2, \dots ,a_{12}\}$ be an Abelian group of order $12$ . Then the order of the element $ ( \prod_{i=1}^{12} a_i)$ is $1$ $2$ $6$ $12$
asked
May 7
in
Set Theory & Algebra
by
Sayan Bose
Loyal
(
7.1k
points)

205
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isi2019mma
engineeringmathematics
discretemathematics
settheory&algebra
groups
0
votes
1
answer
3
ISIMMA201592
Consider the group $G \;=\; \begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{1} \end{pmatrix}\;: a,b \in \mathbb{R},a>0 \end{Bmatrix}$ ... order (D) $N$ is a normal subgroup and the quotient group is isomorphic to $\mathbb{R}^{+}$(the group of positive reals with multiplication).
asked
Mar 6
in
Set Theory & Algebra
by
ankitgupta.1729
Boss
(
15.4k
points)

124
views
groups
groupisomorphism
engineeringmathematics
userisi2015
usermod
+7
votes
4
answers
4
GATE201910
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{1}$ Which of the above is/are equivalence relation/relations? $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
asked
Feb 7
in
Set Theory & Algebra
by
Arjun
Veteran
(
420k
points)

2.5k
views
gate2019
engineeringmathematics
discretemathematics
settheory&algebra
groups
0
votes
0
answers
5
Made Easy Test Series 2019: Set theory & Algebra  Groups
set of all possible diagonal matrix of order n ans given monoid my doubtwhy it cannot have inverse??
asked
Jan 24
in
Set Theory & Algebra
by
priyanka manwani
(
437
points)

72
views
discretemathematics
settheory&algebra
groups
madeeasytestseries2019
madeeasytestseries
0
votes
0
answers
6
Homomorphic and Isomorphic graph
This a random question came into my mind… Are the below statements true: 1] If a graph is Homomorphic to our graph then it is also Isomorphic to that graph. 2]If a graph is Isomorphic to our graph then it is also Homomorphic graph.
asked
Jan 21
in
Set Theory & Algebra
by
Nandkishor3939
Active
(
1.3k
points)

47
views
graphisomorphism
graphtheory
groups
0
votes
0
answers
7
cyclic group
1) 1 2) 2 3) 3 4) 4
asked
Jan 21
in
Mathematical Logic
by
bts1jimin
(
193
points)

57
views
groups
cyclic
0
votes
0
answers
8
group
if (G,*) is a cyclic group of order 97 , then number of generator of G is equal to ___
asked
Jan 16
in
Set Theory & Algebra
by
Rahul_Rathod_
(
421
points)

111
views
groups
discretemathematics
settheory&algebra
0
votes
0
answers
9
Monoid in Group Theory
Is this monoid: Addition modulo (take mode using m) on the set of Integers (Z m)={0,1,2,3,4,…..m1} i.e. For all a a (+ modulo using m) e = e (+ modulo using m) a =a here, e is an identity element
asked
Jan 14
in
Set Theory & Algebra
by
Nandkishor3939
Active
(
1.3k
points)

65
views
groups
discretemathematics
0
votes
0
answers
10
VIRTUAL GATE TEST SERIES
asked
Jan 11
in
Set Theory & Algebra
by
Ajay Maurya 6
(
327
points)

114
views
groups
+1
vote
0
answers
11
#set theory #groups
Consider the set H of all 3 × 3 matrices of the type: $\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$ where a, b, c, d, e and f are real numbers and $abc ≠ 0$. Under the matrix multiplication operation, the set H is: (a) a group (b) a monoid but not a group (c) a semigroup but not a monoid (d) neither a group nor a semigroup
asked
Jan 5
in
Set Theory & Algebra
by
Kunal Kadian
Active
(
2.8k
points)

70
views
settheory&algebra
groups
matrices
0
votes
0
answers
12
Self Doubt[Group Theory]
Is Every Group of Order $P^{k}$ such that P is prime and K is positive integer ABELIAN
asked
Dec 26, 2018
in
Set Theory & Algebra
by
jatin khachane 1
Loyal
(
7k
points)

48
views
discretemathematics
groups
0
votes
1
answer
13
Zeal Test Series 2019: Set Theory & Algebra  Groups
asked
Dec 22, 2018
in
Set Theory & Algebra
by
Prince Sindhiya
Loyal
(
5.5k
points)

60
views
discretemathematics
settheory&algebra
groups
zeal
zeal2019
0
votes
0
answers
14
Group Theory
Lets S1 and S2 be two algebric structure : S1 : {0,1,2,3,4,….,m1},+m1 S2 : {0,1,2,3,4,….,m2},+m1 +m is the addition modulo m. Which of the following are Groups ?
asked
Dec 8, 2018
in
Mathematical Logic
by
Na462
Loyal
(
6.8k
points)

55
views
groups
discretemathematics
+4
votes
1
answer
15
Group theory
Let (G,*) be a group such that O(G) = 8, where O(G) denotes the order of the group. Which of the following is True ? There exist no element a in G whose order is 6. There exist an element a in G whose order is 4. There exist more then one element in G whose order is 1 None of these
asked
Dec 8, 2018
in
Set Theory & Algebra
by
Na462
Loyal
(
6.8k
points)

207
views
groups
discretemathematics
+1
vote
1
answer
16
GATE 2014 MA Groups
asked
Oct 26, 2018
in
Set Theory & Algebra
by
Balaji Jegan
Active
(
4.9k
points)

57
views
groups
0
votes
0
answers
17
GATE 2014 MA Group Theory
Number of nonisomorphic groups of order 10 = ?
asked
Oct 26, 2018
in
Set Theory & Algebra
by
Balaji Jegan
Active
(
4.9k
points)

57
views
groups
0
votes
0
answers
18
Virtual Gate Test Series: Discrete Mathematics  Set Theory & Algebra  Groups
asked
Oct 15, 2018
in
Set Theory & Algebra
by
Prince Sindhiya
Loyal
(
5.5k
points)

46
views
discretemathematics
settheory&algebra
groups
virtualgatetestseries
0
votes
1
answer
19
doubt #Abelian group
reference:Rosen i think two more abelian groups are possible . 1 and 3 are given ,2 and 4 also exist .if i m wrong let me know ,thank you.
asked
Oct 13, 2018
in
Set Theory & Algebra
by
Prateek Raghuvanshi
Boss
(
10.5k
points)

162
views
groups
0
votes
0
answers
20
Cyclic group
The order of cyclic group is equal to order of generating element.... Somebody explain with example plz
asked
Oct 10, 2018
in
Mathematical Logic
by
akankshadewangan24
Active
(
3.9k
points)

126
views
groups
discretemathematics
cyclic
settheory&algebra
+1
vote
1
answer
21
TestBook:Order of Group
How to solve this type of questions??
asked
Oct 7, 2018
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Veteran
(
51.3k
points)

160
views
discretemathematics
settheory&algebra
groups
+2
votes
1
answer
22
Cyclic Group
Suppose that $G$ is a cyclic group of order $10$ with generator $a\in G$.Order of $a^{8}$ is _______
asked
Oct 7, 2018
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Veteran
(
51.3k
points)

189
views
discretemathematics
cyclic
groups
+2
votes
1
answer
23
Groups
If two elements of a group G satisfies $aba^{1} = b^{2}$ for $b\neq e$ then which of the following is equal to $b^{32}$ $A) a^{16}ba^{16}$ $B) a^{5}ba^{5}$ $C) ab^{16}a^{1}$ $D)$ Both $(B)$ and $(C)$
asked
Oct 7, 2018
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Veteran
(
51.3k
points)

78
views
discretemathematics
settheory&algebra
groups
0
votes
1
answer
24
Non isomorphic group of order 10
Number of non isomorphic group of order 10
asked
Sep 27, 2018
in
Set Theory & Algebra
by
Sangeethasiva
(
5
points)

213
views
groups
groupisomorphism
0
votes
1
answer
25
Number of abelian groups
How many different nonisomorphic Abelian groups of order 16 are there?
asked
Sep 22, 2018
in
Set Theory & Algebra
by
Mk Utkarsh
Boss
(
35.2k
points)

123
views
groups
0
votes
0
answers
26
Zeal Workbook: Set Theory & Algebra  Groups
$\text{Prove that : the union of any two subgroup of 'G' is not subgroup of 'G'}$ $\text{Prove that : the intersection of any two subgroup of 'G' is also a subgroup of 'G'}$
asked
Aug 22, 2018
in
Set Theory & Algebra
by
Prince Sindhiya
Loyal
(
5.5k
points)

30
views
discretemathematics
settheory&algebra
groups
zeal
zealworkbook
+1
vote
1
answer
27
Isomorphic Groups
Can Please anybody describe the concept of Isomorphic Groups with an example ? Reference to https://gateoverflow.in/1219/gate200721
asked
May 31, 2018
in
Set Theory & Algebra
by
Na462
Loyal
(
6.8k
points)

134
views
groups
0
votes
1
answer
28
Group Theory
Let G and G1 be two groups such that G1 is a homomorphic image of G. If G is a cyclic group then so is G1.
asked
May 31, 2018
in
Mathematical Logic
by
Sammohan Ganguly
(
311
points)

54
views
groups
0
votes
1
answer
29
Group theory
Let G and G1 be two groups such that G1 is a homomorphic image of G. Prove that if G is a commutative group,then so is G1.
asked
May 31, 2018
in
Mathematical Logic
by
Sammohan Ganguly
(
311
points)

37
views
groups
0
votes
1
answer
30
Group theory
A homomorphism $f:G$ to $G1$ of groups is a monomorphism iff Ker $f = \{e\}$.
asked
May 29, 2018
in
Set Theory & Algebra
by
Sammohan Ganguly
(
311
points)

95
views
engineeringmathematics
discretemathematics
groups
grouphomomorphism
groupmonomorphism
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