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Abstract Algebra
If G = < x > is of order 25, then x^a generates G , where α is a factor of 25.
State the given statement is true or false, give reasons for your answer.
State the given statement is true or false, give reasons for your answer.
Abstract Algebra
If G is a group such that o(G) = 2m , where m∈N , then G has a subgroup of order m.
State the given statement is true or false, give reasons for your answer.
State the given statement is true or false, give reasons for your answer.
Abstract Algebra
If σ is an even permutation, then σ² = I .
State the given statement is true or false, give reasons for your answer.
State the given statement is true or false, give reasons for your answer.
Abstract Algebra
Show that d: Q [x] /{0} --> N Union {0} : d(f) =2 ^(deg f) is a Euclidean valuation on Q [x] .
Abstract Algebra
Consider the ring Homomorphism phi : Z[x] --> (Z/3):phi (summation (n, i =0 ) of a _i x^i ) bar a_0 .Show that Ker phi = (x,3) . What does the Fundamental Theorem of Homomorphism say in this case?
Abstract Algebra
Check whether f : ( 4Z, +) --> ( Z_4, +) : (4m) = bar m is a group Homomorphism or not? If it is, what does the Fundamental Theorem of Homomorphism gives us in this case? If f is not a Homomorphism , obtain the range of f.
Abstract Algebra
How many Sylow 5 - subgroups , Sylow 3 - subgroups and Sylow 2- subgroups can a group of order 200 have ? Give reason for your answer.
Abstract Algebra
Let G be a group , H ∆= G and beta <=(G /H ) . Let A = { x belongs to G | Hx belongs to beta } . Show that (1) . A<=G (2).H ∆= A (3). Beta = (A\H ) .
Abstract Algebra
For x belongs to G , define H _x = { g^(-1) x g | g belongs to G } . Under what conditions on x will H_x <= G ? Further, if H _x <= G , will H_x ∆= G ? Give reason for your answer.
Abstract Algebra
Define a relation R on Z by R={(n,n+3k)| k€Z}.
Check whether R is an equivalence relation or not. If it is, find all the distinct equivalence classes. If R is not an equivalence relation, define an equivalence relation on Z
Check whether R is an equivalence relation or not. If it is, find all the distinct equivalence classes. If R is not an equivalence relation, define an equivalence relation on Z
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#339914 on Dec 2023
#339914 on Dec 2023