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Abstract Algebra
On Q/{-1} define * by a*b=a+b+an for all a,b element of Q/{-1} show that (Q/{-1},*) is an abelian group
Abstract Algebra
Let G={3^n;n element of Z} prove that (G,•)
is an abelian group
is an abelian group
Abstract Algebra
Homomorphism
Abstract Algebra
Show that the polynomial
X5=9x + 3
Is not solvable by radicals over
X5=9x + 3
Is not solvable by radicals over
Abstract Algebra
Show that the polynomial
X5=9x + 3
Is not solvable by radicals over
X5=9x + 3
Is not solvable by radicals over
Abstract Algebra
Show that the polynomial
X^5=9x+3 is not solvable by radicals over
X^5=9x+3 is not solvable by radicals over
Abstract Algebra
Let X be a non-empty set. Define the set Z to be the collection of all subsets of X. Consider the binary operation “union” in the set Z, that is, for A and B that are subsets of X, let
A*B=A∪B
Determine which of the properties of the binary operation is/are satisfied in Z under *.
A*B=A∪B
Determine which of the properties of the binary operation is/are satisfied in Z under *.
Abstract Algebra
Let G=D_8, and let N={e,a^2,a^4,a^6}.
(a) Find all left cosets and all right cosets of N, and verify that N is a normal subgroup of G.
(b) Show that G/N has order 4, but is not cyclic.
(a) Find all left cosets and all right cosets of N, and verify that N is a normal subgroup of G.
(b) Show that G/N has order 4, but is not cyclic.
Abstract Algebra
If A⊂B, prove that (A⋃C)⊂(B⋃C) for any set C.
Abstract Algebra
Show that if g is a non cyclic group of order n then g has no elements of order n. Further give an example with justification of a non cyclic group all of whose proper subgroups are cyclic
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#339914 on Dec 2023
#339914 on Dec 2023