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Recent questions tagged group-theory

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1 answer

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GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.

admin asked in Set Theory & Algebra Feb 15

by admin

1.0k views

1 vote

2 answers

2

GATE CSE 2023 | Memory Based Question: 17
Let $x$ be a set, $2^x=$ power $2 \mathrm{k}$ set of $\mathrm{X}$. define A binary operation $\Delta$ on $2^x$ as $A \Delta B=(A-B) \cup(B-A)$. Let $H=\left(2^x, \Delta\right)$, then for every $A \in 2^x$; inverse of $A$ ... $\mathrm{H}$ is a group. $\mathrm{H}$ satisfies inverse prop, but not a group for every $A \in 2^x$; the inverse of $A$ is $A$.

GO Classes asked in Set Theory & Algebra Feb 6

409 views

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

143 views

0 votes

0 answers

4

Madeasy Test series 2023 Discrete Maths

vishnu777 asked in Mathematical Logic Nov 2, 2022

175 views

1 vote

0 answers

5

Set Theory
If A = {1, 3,5,7,.......} Then (A, +) is semi group or not. Doubt : a +(b+c) =( a + b) +c So associativity property is present But a + b doesn't belong to A So closure property is not present. So A is semi group or not.

Overflow04 asked in Set Theory & Algebra Oct 25, 2022

118 views

0 votes

1 answer

6

Gate At Zeal
Question → If (G,*) is a group of order 960 and there exist a in G such that a^m=e for some integer m<=960 where e is identity element of G then total number of possible value of m is___________ Answer==28

lalitver10 asked in Set Theory & Algebra Sep 17, 2022

231 views

2 votes

1 answer

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 1
What is the order of smallest non-cyclic group?

GO Classes asked in Set Theory & Algebra May 29, 2022

368 views

5 votes

2 answers

8

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 2
Let $\text{G}$ is a cyclic group with generator ‘$a$’. Order of ‘$a$’ is $29.$ The number of subgroups $\text{G}$ has ________

GO Classes asked in Set Theory & Algebra May 29, 2022

298 views

4 votes

1 answer

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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

214 views

3 votes

2 answers

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 4
The set $\{1, 2, 3, \dots , n - 1\}$ is a group under multiplication modulo $n.$ Then the smallest value of $n$ between $20$ and $30$ is $(20, 30$ included $)\;$ _______

GO Classes asked in Set Theory & Algebra May 29, 2022

241 views

2 votes

2 answers

11

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 5
Consider the group $0,1,2,3,4,+{ }_{5}$. What will be the value of $2^{-3}$ and $3^{-2}$ for the given group? $1$ and $1$ $2$ and $3$ $4$ and $4$ $3$ and $2$

GO Classes asked in Set Theory & Algebra May 29, 2022

193 views

3 votes

1 answer

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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

160 views

3 votes

2 answers

13

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 8
Which of the following associative multiplication tables defined on the set $G = \{a, b, c, d\}$ form a group?

GO Classes asked in Set Theory & Algebra May 29, 2022

285 views

4 votes

1 answer

14

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 9
The group $Z_{n}$ consists of the elements $\{0,1,2, \ldots, n-1\}$ with addition $\bmod n$ as the operation. How many subgroups of $Z_{9}$ are there?

GO Classes asked in Set Theory & Algebra May 29, 2022

147 views

3 votes

1 answer

15

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 10
Let $Z$ be the set of all integers. Let $n \in Z$ and $nZ = {nk : k \in Z}.$ Which of the following is/are true? $nZ$ is a subgroup of $Z$ (under addition operation) for all $n \in Z.$ Every subgroup of ... some $n.$ $3Z$ is the smallest subgroup of $(Z,+)$ containing $3.$ $nZ$ is a cyclic subgroup of $Z.$

GO Classes asked in Set Theory & Algebra May 29, 2022

270 views

4 votes

1 answer

16

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 11
The set $Z_{\mathrm{n}}^{*}$ consists of the elements $\{1,2, \ldots, \mathrm{n}-1\}$ with multiplication $\bmod n$ as the operation. The group $Z_{n}$ consists of the elements $\{0,1,2, \ldots, n-1\}$ ... then $\mathrm{G}$ is a cyclic group. The number of elements in $Z_{8}^{*}$ which have an inverse is $4.$

GO Classes asked in Set Theory & Algebra May 29, 2022

152 views

2 votes

1 answer

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 12
Consider the standard groups $Z_{\mathrm{n}}, \mathrm{R}^{*}, \mathrm{C}^{*}$ under their standard group operation. Here, $\mathrm{R}^{*}, \mathrm{C}^{*}$ are set of non-zero real numbers, set of non-zero complex numbers, ... $\sqrt{3} \in \mathrm{R}^{*}$ $-\mathrm{i} \in \mathrm{C}^{*}$

GO Classes asked in Set Theory & Algebra May 29, 2022

149 views

1 vote

1 answer

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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

225 views

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