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Recent questions tagged group-theory
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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
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lalitver10
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2
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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?
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5
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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 ________
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May 29
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GO Classes
179
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goclasses_wq12
numerical-answers
goclasses
set-theory&algebra
group-theory
cyclic-group
1-mark
4
votes
1
answer
4
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
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May 29
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GO Classes
119
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goclasses_wq12
goclasses
set-theory&algebra
group-theory
abelian-group
1-mark
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 $)\;$ _______
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May 29
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GO Classes
134
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goclasses_wq12
numerical-answers
goclasses
set-theory&algebra
group-theory
1-mark
2
votes
2
answers
6
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 $2$
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in
Set Theory & Algebra
May 29
by
GO Classes
118
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goclasses_wq12
goclasses
set-theory&algebra
group-theory
1-mark
3
votes
1
answer
7
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
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Set Theory & Algebra
May 29
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GO Classes
94
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goclasses_wq12
goclasses
set-theory&algebra
group-theory
abelian-group
2-marks
3
votes
2
answers
8
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?
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Set Theory & Algebra
May 29
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GO Classes
139
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goclasses_wq12
goclasses
set-theory&algebra
group-theory
multiple-selects
2-marks
4
votes
1
answer
9
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
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Set Theory & Algebra
May 29
by
GO Classes
81
views
goclasses_wq12
numerical-answers
goclasses
set-theory&algebra
group-theory
2-marks
3
votes
1
answer
10
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
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May 29
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GO Classes
151
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goclasses_wq12
goclasses
set-theory&algebra
group-theory
group-isomorphism
multiple-selects
2-marks
4
votes
1
answer
11
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
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in
Set Theory & Algebra
May 29
by
GO Classes
85
views
goclasses_wq12
goclasses
set-theory&algebra
group-theory
multiple-selects
2-marks
2
votes
1
answer
12
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
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in
Set Theory & Algebra
May 29
by
GO Classes
81
views
goclasses_wq12
goclasses
set-theory&algebra
group-theory
multiple-selects
2-marks
1
vote
1
answer
13
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
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in
Set Theory & Algebra
May 29
by
GO Classes
103
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goclasses_wq12
goclasses
set-theory&algebra
group-theory
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Sir some test due date passed 1-2 months ago pls...
@lalitver10 There is no restriction in doing...
@GateOverflow04 link fixed now.
@Arjun @Deepak Sir, In Test Schedule google...
sir is this for gate? it has way more questions...