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Recent questions tagged group-theory

1 votes
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151
Group Theory
Let G and G1 be two groups such that G1 is a homomorphic image of G. If G is a cyclic group then so is G1.
Let G and G1 be two groups such that G1 is a homomorphic image of G.If G is a cyclic group then so is G1.
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1 votes
1 answer
152
Group theory
Let G and G1 be two groups such that G1 is a homomorphic image of G. Prove that if G is a commutative group,then so is G1.
Let G and G1 be two groups such that G1 is a homomorphic image of G.Prove that if G is a commutative group,then so is G1.
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0 votes
0 answers
154
group theory and cryptography
How is group theory and cryptography linked?
How is group theory and cryptography linked?
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1 votes
1 answer
155
Group Theory
Prove that :- Every infinite cyclic group is isomorphic to the infinite cyclic group of integers under addition.
Prove that :-Every infinite cyclic group is isomorphic to the infinite cyclic group of integers under addition.
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8 votes
3 answers
157
ISRO2018-17
$(\text{G}, \ast )$ is an abelian group. Then $x= x^{-1}$ for any $x$ belonging to $\text{G}$ $x=x^{2}$ for any $x$ belonging to $\text{G}$ $\left( x \ast y \right )^{2}= x^{2} \ast y^{2}$ , for any $x, y$ belonging to $\text{G}$ $\text{G}$ is of finite order
$(\text{G}, \ast )$ is an abelian group. Then$x= x^{-1}$ for any $x$ belonging to $\text{G}$$x=x^{2}$ for any $x$ belonging to $\text{G}$$\left( x \ast y \right )^{2}= x^...
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28 votes
4 answers
159
GATE CSE 2018 | Question: 19
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
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1 votes
1 answer
160
Graph theory
If $N=(0,1,2,3 ....)$ , then $(N,+)$ is a Group. If $N=(1,2,3 ....)$ , then $(N,+)$ is a not Group. Which one to consider in exam ?
If $N=(0,1,2,3 ....)$ , then $(N,+)$ is a Group.If $N=(1,2,3 ....)$ , then $(N,+)$ is a not Group.Which one to consider in exam ?
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2 votes
1 answer
161
non abelian
Let G be a non abelian group, order of G can be 24 44 54 34
Let G be a non abelian group, order of G can be 24 44 54 34
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2 votes
1 answer
163
Check which one is this
The binary operation defined on a,b∈z such that a*b= min⁡(a,b)then (A,*) is a)monoid b)group c)algebric-structure d)semi group
The binary operation defined on a,b∈z such that a*b= min⁡(a,b)then (A,*) isa)monoidb)groupc)algebric-structured)semi group
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0 votes
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164
Group
A set of odd integers under the operation of multiplication forms A) A group but not abelian group B) A monoid but not group C) Semigroup but not monoid D) Abelian group
A set of odd integers under the operation of multiplication formsA) A group but not abelian groupB) A monoid but not groupC) Semigroup but not monoidD) Abelian group
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2 votes
0 answers
165
group
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1 votes
1 answer
166
Cyclic Group
Find all the subgroups of a cyclic group of order 12. (A) {e},(a6),(a4),(a3),(a2),(a) (B) (a12),(a6),(a4),(a3),(a2),(a) (C) (a12),(a6),(a4),(a2),(a) (D) (a12),(a6),(a4),(a3),(a2),(a),{e}
Find all the subgroups of a cyclic group of order 12.(A) {e},(a6),(a4),(a3),(a2),(a)(B) (a12),(a6),(a4),(a3),(a2),(a)(C) (a12),(a6),(a4),(a2),(a)(D) (a12),(a6),(a4),(a3),...
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2 votes
0 answers
168
Group Theory
Let G be a finite group.If A and B are subgroups of G with orders 4 and 5 respectively then |A$\cap$B|=......
Let G be a finite group.If A and B are subgroups of G with orders 4 and 5 respectively then |A$\cap$B|=......
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4 votes
1 answer
169
Group Theory
Assume g is an element of the group.consider the following conditions of g with e as identity element. 1.g8=e 2.g2$\neq$e 3.Order of g is not 8. Find the order of g.
Assume g is an element of the group.consider the following conditions of g with e as identity element.1.g8=e2.g2$\neq$e3.Order of g is not 8.Find the order of g.
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0 votes
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170
Group Question
If a, b are elements of a group G, then (ba)-1 =
If a, b are elements of a group G, then (ba)-1 =
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1 votes
0 answers
172
testbook test series
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7 votes
2 answers
173
Group theory doubt
1)Suppose that G is cyclic group of order 10 with generator a €G .Order of a^8 is... 2)(G,*) is an abelian group which of the following must hold A)for all g€G. g-1 = g B)for all g€G. g^2 =e C)for all a,b €G ( a*b)^2 =a^2* b^2
1)Suppose that G is cyclic group of order 10 with generator a €G .Order of a^8 is...2)(G,*) is an abelian group which of the following must hold A)for all g€G. g-...
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3 votes
0 answers
174
Self Doubt
Let < G, * > be a finite group and let H1 and H2 be it's sub group as per lagrange theorem we know order of sub group divides order of group, my doubt is, is it possible that we can have multiple subgroup of same cardinality for a particular group ? $\left | H1 \right |=\left | H2 \right |$
Let < G, * be a finite group and let H1 and H2 be it's sub group as per lagrange theorem we know order of sub group divides order of group, my doubt is, is it possible t...
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1 votes
1 answer
176
#GroupTheory #TestBook
Plz explain this question
Plz explain this question
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1 votes
0 answers
179
group
what is the group in properties of closure properties in automata??
what is the group in properties of closure properties in automata??
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4 votes
3 answers
180
[Discrete Maths] Group Theory
If the group has 40 elements and it has two subgroups namely h and k with order 10 and 20 then what can't be order of (h intersection k) a:)10 b:)20 c:)3 d:)1 e:) 4 My answer is both c and b and e. Is it correct?
If the group has 40 elements and it has two subgroups namely h and k with order 10 and 20 then what can't be order of (h intersection k)a:)10b:)20c:)3d:)1e:) 4My answer i...
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