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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
+1
vote
4
answers
1
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
(
385k
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1.9k
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gate2019
engineeringmathematics
discretemathematics
settheory&algebra
groups
0
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0
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2
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
(
1.2k
points)

31
views
graphisomorphism
graphtheory
groups
0
votes
0
answers
3
cyclic group
1) 1 2) 2 3) 3 4) 4
asked
Jan 21
in
Mathematical Logic
by
bts1jimin
(
245
points)

44
views
groups
cyclic
0
votes
0
answers
4
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_
Junior
(
565
points)

73
views
groups
discretemathematics
settheory&algebra
0
votes
0
answers
5
Groups
How G = ( 1,1,i,  i ) under multiplication is Group? H = ( i, i ) is subgroup under multiplication? Please suggest
asked
Jan 15
in
Set Theory & Algebra
by
Mayankprakash
Active
(
1.1k
points)

36
views
settheory&algebra
subgroups
groups
discretemathematics
0
votes
0
answers
6
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
(
1.2k
points)

51
views
groups
discretemathematics
0
votes
0
answers
7
VIRTUAL GATE TEST SERIES
asked
Jan 11
in
Set Theory & Algebra
by
Ajay Maurya 6
(
197
points)

94
views
groups
+1
vote
0
answers
8
#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
(
2.6k
points)

56
views
settheory&algebra
groups
matrices
0
votes
0
answers
9
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
(
6.4k
points)

38
views
discretemathematics
groups
0
votes
0
answers
10
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
(
8.6k
points)

48
views
groups
discretemathematics
+4
votes
1
answer
11
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
(
8.6k
points)

147
views
groups
discretemathematics
+1
vote
1
answer
12
GATE 2014 MA Groups
asked
Oct 26, 2018
in
Set Theory & Algebra
by
Balaji Jegan
Active
(
4.8k
points)

47
views
groups
0
votes
0
answers
13
GATE 2014 MA Group Theory
Number of nonisomorphic groups of order 10 = ?
asked
Oct 26, 2018
in
Set Theory & Algebra
by
Balaji Jegan
Active
(
4.8k
points)

45
views
groups
0
votes
1
answer
14
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
Loyal
(
9.7k
points)

148
views
groups
0
votes
0
answers
15
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
(
4.3k
points)

85
views
groups
discretemathematics
cyclic
settheory&algebra
+1
vote
1
answer
16
TestBook:Order of Group
How to solve this type of questions??
asked
Oct 7, 2018
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
29k
points)

144
views
discretemathematics
settheory&algebra
groups
+2
votes
1
answer
17
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
Boss
(
29k
points)

155
views
discretemathematics
cyclic
groups
+2
votes
1
answer
18
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
Boss
(
29k
points)

60
views
discretemathematics
settheory&algebra
groups
0
votes
1
answer
19
Non isomorphic group of order 10
Number of non isomorphic group of order 10
asked
Sep 27, 2018
in
Set Theory & Algebra
by
Sangeethasiva
(
7
points)

126
views
groups
groupisomorphism
0
votes
1
answer
20
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
(
34.1k
points)

80
views
groups
0
votes
1
answer
21
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
(
8.6k
points)

99
views
groups
0
votes
1
answer
22
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
(
455
points)

46
views
groups
0
votes
1
answer
23
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
(
455
points)

34
views
groups
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