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Recent questions tagged group-theory

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group
what is the group in properties of closure properties in automata??
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[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:)10b:)20c:)3d:)1e:) 4My answer is both c and b and e. Is it correct?
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[Discrete maths ] Group theory
Let G be abelian, H and K subgroups of G with orders n, m. Then G has subgroup of order lcm(n,m)I have gone through prrof here:- https:// ... examples where n divides G but there is no subgroup with that order.Please clear with explanation.
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[Discrete maths] Group Theory
Can the following operation be used with a non empty set to represent a group?a*b=sqrt($a^{2}+b^{2}$)My doubt is,does this operation represents a function or do we include +- sign both as output ?
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Test by Bikram | Mock GATE | Test 4 | Question: 21
$\left ( G, . \right )$ is a group such that $\left ( x,y \right )^{-1} = x^{-1}y^{-1}, \forall \left ( x,y \right ) \in G$.Here, $G$ is a: Monoid Commutative semi group Abelian group Semi group
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keneth r rosen discrete mathematics
the relation R is partial order on the set Z where, R is defined as, a R b iff a=2b.how to prove it.
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keneth r rosen discrete mathematics
IF H be a subgroup of a group G then how to prove that the relationR= {(x,y): x,y belong to G, x-1ybelongs to H} is an equivalence relation.Please help as soon as possible.
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keneth r rosen discrete mathematics
In a group G, how to prove that (a.b)-1 = b-1. a-1 for all a,b belongs to G.
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keneth r rosen discrete mathematics
how to prove lagrange's theorem in groups?
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group theory
"the union of two sub-groups neednot be a sub-group".can some-body prove without using counter example ...
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group theory
"The necessary and sufficient condition for a subset of a group to be called as sub-group is it should satisfy the algebraic structure property".can ... structure property satisfying and not checking for identity element,inverse ....why ?
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group theory
which among the following statements is TRUE ?S1 : ( { 0,1,2....(m-1) } , +m ) where +m stands for "addition-modulo-m"S2 : ( {0,1,2....m} , +m ) where ... .B) ONLY S2 is a group.C) BOTH S1 AND S2 are groups.D) NEITHER S1 NOT S2 is a group.
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group theory
Is ( {0},* ) a group ? ( where * stands for multiplication operation ).Please provide explanations with your answer
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Group Theory discrete maths
A={1,2,3,4,5,6}Given that set A is a group with respect to multiplication mod 7.Is A a cyclic group?If yes,identify the generators.Is there any theorem that i cana pply here to solve without building operation table?
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Self doubt
Is there any valid group for which cayley table will have duplicate entry in row or column.???Or we can say that for each valid finite group ut will have ... table in which each row and column has all elements of group without repititon.??
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Test by Bikram | Mock GATE | Test 2 | Question: 21
Which of the following statements are false?The order of any finite group is always divisible by the order of the subgroups.Intersection of two subgroups of a group ... proper and improper subgroups.III and IVII and IVI and IIII, III, IV
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GROUP THEORY
Can someone tell whether these topics are important in GROUP THEORY?ISOMORPHIC GROUPSNORMAL GROUPSCOSETS.
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geek mock 2017 #38
Let A = { 1,2,3,4, .∞ } and a binary operation +' is defined by a + b = ab ∀ a,b ∈ A. Which of the following is true ?( A, + ) is a ... ( A, + ) is not a semi grou i think it should be semigroup because we dont have an identity element
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matrix groups
Which of the following is true?Every lower triangular matrix is group under multiplication operation where all elements of diagonal are non zero numbers.Every diagonal matrix is group ... numbers.Both (a) and b)isn't a b c all are correct?
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Test series Testbook
Is this a distributive lattice????
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GATE CSE 1988 | Question: 13ic
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$f(x)=x^3$, for all $x$ belonging to $G$.
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GATE CSE 1988 | Question: 13ib
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$\overline{G}=G$
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GATE CSE 1988 | Question: 13ia
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$G$ is the group of non zero real numbers under multiplication.
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GATE CSE 1988 | Question: 2xviii
Show that if $G$ is a group such that $(a. b)^2 = a^2.b^2$ for all $a, b$ belonging to $G$, then $G$ is an abelian.
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MadeEasy Test Series: Set Theory & Algebra - Groups
Which of the following is true?Every lower triangular matrix is group under multiplication operation where all elements of diagonal are non zero numbers.Every diagonal matrix ... elements are real numbers.Both (a) and b)Why is C incorrect?
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the number of generators of the group { 0,1,2........... 14} under the group operation addition modulu 15 is
the number of generators of the group { 0,1,2........... 14} under the group operation addition modulu 15 is
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GATE CSE 1990 | Question: 2-x
Match the pairs in the following questions: ...
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GATE CSE 1987 | Question: 9f
Give the composition tables (Cayley Tables) of the two non-isomorphic groups of order $4$ with elements $e, a, b, c$ where $c$ is the identity element. Use the order $e, a, b, c$ for the rows and columns.
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General Topic Doubt Set Theory & Algebra: Groups
In the above question my doubt is instead of under multiplication if we change under ADDITION then what is its value?plz someone explain details.
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Permutation groups
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