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Recent questions tagged group-theory

0 votes

3 answers

121

ISI2015-MMA-92
Consider the group $G=\begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{-1} \end{pmatrix} : a,b \in \mathbb{R}, \: a>0 \end{Bmatrix}$ ... is of finite order $N$ is a normal subgroup and the quotient group is isomorphic to $\mathbb{R}^+$ (the group of positive reals with multiplication).

Arjun asked in Set Theory & Algebra Sep 23, 2019

by Arjun

1.4k views

3 votes

1 answer

122

ISI2015-MMA-93
Let $G$ be a group with identity element $e$. If $x$ and $y$ are elements in $G$ satisfying $x^5y^3=x^8y^5=e$, then which of the following conditions is true? $x=e, \: y=e$ $x\neq e, \: y=e$ $x=e, \: y \neq e$ $x\neq e, \: y \neq e$

Arjun asked in Set Theory & Algebra Sep 23, 2019

by Arjun

875 views

0 votes

1 answer

123

ISI2015-MMA-94
Let $G$ be the group $\{\pm1, \pm i \}$ with multiplication of complex numbers as composition. Let $H$ be the quotient group $\mathbb{Z}/4 \mathbb{Z}$. Then the number of nontrivial group homomorphisms from $H$ to $G$ is $4$ $1$ $2$ $3$

Arjun asked in Set Theory & Algebra Sep 23, 2019

by Arjun

794 views

3 votes

3 answers

124

ISI2018-MMA-15
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.

akash.dinkar12 asked in Set Theory & Algebra May 11, 2019

by akash.dinkar12

3.1k views

2 votes

3 answers

125

ISI2019-MMA-19
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 $1$ $2$ $6$ $12$

Sayan Bose asked in Set Theory & Algebra May 7, 2019

2.1k views

37 votes

9 answers

126

GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$

Arjun asked in Set Theory & Algebra Feb 7, 2019

by Arjun

17.3k views

1 vote

1 answer

127

Made Easy Test Series 2019: Set theory & Algebra - Groups
set of all possible diagonal matrix of order n ans given monoid my doubt-why it cannot have inverse??

priyanka manwani asked in Set Theory & Algebra Jan 24, 2019

by priyanka manwani

627 views

1 vote

1 answer

128

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.

Nandkishor3939 asked in Set Theory & Algebra Jan 21, 2019

by Nandkishor3939

1.0k views

1 vote

1 answer

129

cyclic group
1-) 1 2-) 2 3-) 3 4-) 4

bts1jimin asked in Mathematical Logic Jan 21, 2019

455 views

2 votes

2 answers

130

group
if (G,*) is a cyclic group of order 97 , then number of generator of G is equal to ___

Rahul_Rathod_ asked in Set Theory & Algebra Jan 16, 2019

by Rahul_Rathod_

1.5k views

0 votes

0 answers

131

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,…..m-1} i.e. For all a a (+ modulo using m) e = e (+ modulo using m) a =a here, e is an identity element

Nandkishor3939 asked in Set Theory & Algebra Jan 13, 2019

by Nandkishor3939

860 views

2 votes

2 answers

132

VIRTUAL GATE TEST SERIES

Ajay Maurya 6 asked in Set Theory & Algebra Jan 10, 2019

by Ajay Maurya 6

1.1k views

4 votes

2 answers

133

#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

Kunal Kadian asked in Set Theory & Algebra Jan 5, 2019

by Kunal Kadian

575 views

0 votes

0 answers

134

Self Doubt[Group Theory]
Is Every Group of Order $P^{k}$ such that P is prime and K is positive integer ABELIAN

jatin khachane 1 asked in Set Theory & Algebra Dec 26, 2018

by jatin khachane 1

511 views

2 votes

2 answers

135

Zeal Test Series 2019: Set Theory & Algebra - Groups

Prince Sindhiya asked in Set Theory & Algebra Dec 21, 2018

by Prince Sindhiya

540 views

1 vote

0 answers

136

Zeal Test Series 2019: Set Theory & Algebra - Sets

Prince Sindhiya asked in Set Theory & Algebra Dec 21, 2018

by Prince Sindhiya

497 views

0 votes

0 answers

137

Group Theory
Lets S1 and S2 be two algebric structure : S1 : {0,1,2,3,4,….,m-1},+m-1 S2 : {0,1,2,3,4,….,m-2},+m-1 +m is the addition modulo m. Which of the following are Groups ?

Na462 asked in Mathematical Logic Dec 8, 2018

by Na462

393 views

6 votes

2 answers

138

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

Na462 asked in Set Theory & Algebra Dec 8, 2018

by Na462

3.1k views

1 vote

1 answer

139

GATE 2014 MA Groups

Balaji Jegan asked in Set Theory & Algebra Oct 26, 2018

by Balaji Jegan

283 views

0 votes

0 answers

140

GATE 2014 MA Group Theory
Number of non-isomorphic groups of order 10 = ?

Balaji Jegan asked in Set Theory & Algebra Oct 26, 2018

by Balaji Jegan

481 views

1 vote

1 answer

141

Virtual Gate Test Series: Discrete Mathematics - Set Theory & Algebra - Groups

Prince Sindhiya asked in Set Theory & Algebra Oct 15, 2018

by Prince Sindhiya

571 views

0 votes

1 answer

142

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.

Prateek Raghuvanshi asked in Set Theory & Algebra Oct 13, 2018

by Prateek Raghuvanshi

1.1k views

1 vote

2 answers

143

Cyclic group
The order of cyclic group is equal to order of generating element.... Somebody explain with example plz

akankshadewangan24 asked in Mathematical Logic Oct 10, 2018

by akankshadewangan24

1.0k views

1 vote

1 answer

144

TestBook:Order of Group
How to solve this type of questions??

Lakshman Bhaiya asked in Set Theory & Algebra Oct 7, 2018

by Lakshman Bhaiya

1.5k views

5 votes

1 answer

145

Cyclic Group
Suppose that $G$ is a cyclic group of order $10$ with generator $a\in G$.Order of $a^{8}$ is _______

Lakshman Bhaiya asked in Set Theory & Algebra Oct 7, 2018

by Lakshman Bhaiya

2.1k views

2 votes

1 answer

146

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 $(C)$

Lakshman Bhaiya asked in Set Theory & Algebra Oct 7, 2018

by Lakshman Bhaiya

542 views

2 votes

2 answers

147

Non isomorphic group of order 10
Number of non isomorphic group of order 10

Sangeethasiva asked in Set Theory & Algebra Sep 27, 2018

by Sangeethasiva

2.6k views

1 vote

1 answer

148

Number of abelian groups
How many different non-isomorphic Abelian groups of order 16 are there?

Mk Utkarsh asked in Set Theory & Algebra Sep 22, 2018

1.1k views

1 vote

0 answers

149

Zeal Workbook: Set Theory & Algebra - Groups
$\text{Prove that : the union of any two subgroup of 'G' is not subgroup of 'G'}$ $\text{Prove that : the intersection of any two subgroup of 'G' is also a subgroup of 'G'}$

Prince Sindhiya asked in Set Theory & Algebra Aug 22, 2018

by Prince Sindhiya

328 views

1 vote

1 answer

150

Isomorphic Groups
Can Please anybody describe the concept of Isomorphic Groups with an example ? Reference to https://gateoverflow.in/1219/gate2007-21

Na462 asked in Set Theory & Algebra May 31, 2018

by Na462

991 views

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Recent questions tagged group-theory