Recent questions tagged group-theory

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1

$\textbf{NTA NET DEC 2019 (group)}$
Consider the following statements: $\mathbf{S_1:}\;\;$If a group $\mathbf{(G,*)}$ is of order $\mathbf n$ and $\mathrm {a \in G}$ is such that $\mathrm {a^n=e}$ for some integer $\mathrm {m \le n}$ then $\mathbf m$ must divide $\mathbf n$ ... $(3)\;\;\;\text{Niether}\; \mathrm{S_1}\;\text{nor}\;\mathrm{S_2}$

asked Dec 29, 2019 in Set Theory & Algebra by Sanjay Sharma Boss (49.3k points) | 95 views

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0 answers

2

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).

asked Sep 23, 2019 in Set Theory & Algebra by Arjun Veteran (430k points) | 21 views

0 votes

1 answer

3

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? $x=e, \: y=e$ $x\neq e, \: y=e$ $x=e, \: y \neq e$ $x\neq e, \: y \neq e$

asked Sep 23, 2019 in Set Theory & Algebra by Arjun Veteran (430k points) | 27 views

0 votes

1 answer

4

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 $4$ $1$ $2$ $3$

asked Sep 23, 2019 in Set Theory & Algebra by Arjun Veteran (430k points) | 19 views

0 votes

1 answer

5

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.

asked May 11, 2019 in Set Theory & Algebra by akash.dinkar12 Boss (42.4k points) | 94 views

+1 vote

1 answer

6

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 $1$ $2$ $6$ $12$

asked May 7, 2019 in Set Theory & Algebra by Sayan Bose Loyal (7.4k points) | 241 views

0 votes

1 answer

7

ISI-MMA-2015-92
Consider the group $G \;=\; \begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{-1} \end{pmatrix}\;: a,b \in \mathbb{R},a>0 \end{Bmatrix}$ ... 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, 2019 in Set Theory & Algebra by ankitgupta.1729 Boss (17k points) | 140 views

+11 votes

3 answers

8

GATE2019-10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{-1}$ 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, 2019 in Set Theory & Algebra by Arjun Veteran (430k points) | 3.4k views

0 votes

0 answers

9

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??

asked Jan 24, 2019 in Set Theory & Algebra by priyanka manwani (453 points) | 85 views

0 votes

0 answers

10

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, 2019 in Set Theory & Algebra by Nandkishor3939 Active (1.3k points) | 61 views

0 votes

0 answers

11

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

asked Jan 21, 2019 in Mathematical Logic by bts1jimin (205 points) | 70 views

0 votes

1 answer

12

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

asked Jan 16, 2019 in Set Theory & Algebra by Rahul_Rathod_ (431 points) | 138 views

0 votes

0 answers

13

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

asked Jan 14, 2019 in Set Theory & Algebra by Nandkishor3939 Active (1.3k points) | 83 views

+1 vote

0 answers

14

VIRTUAL GATE TEST SERIES

asked Jan 11, 2019 in Set Theory & Algebra by Ajay Maurya 6 (405 points) | 130 views

+1 vote

2 answers

15

#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, 2019 in Set Theory & Algebra by Kunal Kadian Active (2.8k points) | 81 views

0 votes

0 answers

16

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 (7.4k points) | 57 views

0 votes

1 answer

17

Zeal Test Series 2019: Set Theory & Algebra - Groups

asked Dec 22, 2018 in Set Theory & Algebra by Prince Sindhiya Loyal (5.9k points) | 75 views

0 votes

0 answers

18

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 ?

asked Dec 8, 2018 in Mathematical Logic by Na462 Loyal (7k points) | 64 views

+4 votes

1 answer

19

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 (7k points) | 269 views

+1 vote

1 answer

20

GATE 2014 MA Groups

asked Oct 26, 2018 in Set Theory & Algebra by Balaji Jegan Active (5k points) | 73 views

0 votes

0 answers

21

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

asked Oct 26, 2018 in Set Theory & Algebra by Balaji Jegan Active (5k points) | 68 views

0 votes

0 answers

22

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

asked Oct 15, 2018 in Set Theory & Algebra by Prince Sindhiya Loyal (5.9k points) | 57 views

0 votes

1 answer

23

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 (10.8k points) | 175 views

0 votes

0 answers

24

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 (4k points) | 161 views

+1 vote

1 answer

25

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

asked Oct 7, 2018 in Set Theory & Algebra by Lakshman Patel RJIT Veteran (58.7k points) | 176 views

+2 votes

1 answer

26

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 (58.7k points) | 221 views

+2 votes

1 answer

27

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 (58.7k points) | 87 views

0 votes

1 answer

28

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) | 275 views

0 votes

1 answer

29

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

asked Sep 22, 2018 in Set Theory & Algebra by Mk Utkarsh Boss (36.4k points) | 143 views

0 votes

0 answers

30

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 (5.9k points) | 33 views

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