For the following exercises, find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in terms of x and y.) 177. x 3 + y 3 = 3 x y z , P ( 1 , 2 3 2 )
For the following exercises, find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in terms of x and y.) 177. x 3 + y 3 = 3 x y z , P ( 1 , 2 3 2 )
Topic: Group Theory | Abstract Algebra
Question:
Let G be a finite group of order 45. Prove that G has a normal subgroup of order 5 or order 9, and describe
the number of Sylow subgroups for each.
Instructions:
•
Use Sylow's Theorems (existence, conjugacy, and counting).
•
List divisors of 45 and compute possibilities for n for p = 3 and p = 5.
Show that if n = 1, the subgroup is normal.
Conclude about group structure using your analysis.
Topic: Group Theory | Abstract Algebra
Question:
Let G be a finite group of order 45. Prove that G has a normal subgroup of order 5 or order 9, and describe
the number of Sylow subgroups for each.
Instructions:
•
Use Sylow's Theorems (existence, conjugacy, and counting).
•
List divisors of 45 and compute possibilities for n for p = 3 and p = 5.
Show that if n = 1, the subgroup is normal.
Conclude about group structure using your analysis.
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
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