Recent questions tagged group-theory

Recent questions tagged group-theory

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

99 views

4 votes

2 answers

2

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

76 views

3 votes

1 answer

3

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

54 views

3 votes

2 answers

4

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

49 views

2 votes

2 answers

5

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

50 views

3 votes

1 answer

6

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

45 views

3 votes

1 answer

7

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

47 views

3 votes

1 answer

8

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

41 views

3 votes

1 answer

9

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

80 views

4 votes

1 answer

10

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

43 views

2 votes

1 answer

11

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

36 views

1 vote

1 answer

12

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

36 views

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