(adsbygoogle = window.adsbygoogle || []).push({}); Abstract Algebra Questions - Need help for exam!!

1. The problem statement, all variables and given/known data

I am studying Abstract Algebra in college and my exams are approaching fast.I need somebody to help me out to do a few exam papers.

I am going to post the questions below from the exam papers and if you can advise me how to do do them , just post what to do.I dont think that they are that difficult and if you have a good grasp of the algebra they are fairly doable.

Q1

State clearly the general definition of an equivalence relation. Show that

(a, b) ~(r, s) iff a + s = b + r

defines an equivalence relation on the set M = {1, 2, 3, 4, . . .}×{1, 2, 3, 4, . . .},

which contains precisely all pairs of positive integers.

Q2

(b) State clearly Lagrange’s Theorem.

Find all subgroups of the symmetric group S3.

(c) Prove that {1, t, t2, t3, t4, t55 marks } is a normal subgroup of the dihedral group D6.

Q3

State Euler’s theorem and use it to compute 254477550 mod 282.

Q4

Prove that the multiplicative group (Z/24Z)* is not isomorphic to the additive group (Z/8Z).

Q5

Write = (1 4 8 7)(3 4)(1 8 5) element of S8 as a product of cycles with disjoint trace.

Determine the order ord() and parity sgn() of the permutation . Write its

inverse −1 as a product of cycles with disjoint trace.

All help would be appreciated. I dont think that they are too difficult but like everything in maths its just a matter of knowing how to do them..

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Abstract Algebra Questions - Need help for exam

**Physics Forums | Science Articles, Homework Help, Discussion**