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Recent questions tagged group-theory
2
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2
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GATE CSE 2024 | Set 2 | Question: 53
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ that are their own inverses is ___________.
Arjun
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Set Theory & Algebra
Feb 16
by
Arjun
1.8k
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gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
3
votes
1
answer
2
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 28
A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarily finite cyclic abelian none of the above
GO Classes
asked
in
Set Theory & Algebra
Jan 28
by
GO Classes
317
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
1-mark
3
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0
answers
3
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 61
Let $S$ be the set of all functions $f: \mathbb{R} \rightarrow \mathbb{R}$. Consider the two binary operations + and $\circ$ on $S$ ... law $(g+h) \circ f=(g \circ f)+(h \circ f)$. None III only II and III only I, II, and III
GO Classes
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in
Set Theory & Algebra
Jan 28
by
GO Classes
408
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
2-marks
2
votes
1
answer
4
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 19
Let $\ast $ be the binary operation on the rational numbers given by $a \ast b=a+b+2 a b$. Which of the following are true? $\ast $ is commutative There is a rational number that is a $\ast \;-$ identity. Every rational number has a $\ast \;-$ inverse. I only I and II only I and III only I, II, and III
GO Classes
asked
in
Set Theory & Algebra
Jan 21
by
GO Classes
443
views
goclasses2024-mockgate-12
goclasses
set-theory&algebra
group-theory
1-mark
2
votes
1
answer
5
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 37
If $b$ and $c$ are elements in a group $G$, and if $b^5=c^3=e$, where $e$ is the unit element of $G$, then the inverse of $b^2 c b^4 c^2$ must be $b^4 c^2 b^2 c$ $c^2 b^4 c b^2$ $c b^2 c^2 b^4$ $c b c^2 b^3$
GO Classes
asked
in
Set Theory & Algebra
Jan 13
by
GO Classes
401
views
goclasses2024-mockgate-11
goclasses
set-theory&algebra
group-theory
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