Math Is Fun Forum

loida

Member

Registered: 2009-11-12

Posts: 32

Algebra problem

if anybody knows this, pls help...

1. determine a group of Aut((Z/2Z) ⊕ (Z/2Z))  (prove every statement)

2.show that cycle (of length n) is even permutation if and only if n is an odd number

3. G={a1, a2, ..., an } finite abelian group. Is it always (a1 a2 .... an)^2=e ?

scientia

Member

Registered: 2009-11-13

Posts: 224

Re: Algebra problem

if anybody knows this, pls help...

1. determine a group of Aut((Z/2Z) ⊕ (Z/2Z))  (prove every statement)

2.show that cycle (of length n) is even permutation if and only if n is an odd number

3. G={a1, a2, ..., an } finite abelian group. Is it always (a1 a2 .... an)^2=e ?

1. This is the automorphism group of the Klein 4-group; I think it is

but you will need to verify it.

2. Hint: A cycle of length n can be written as a product of n−1 transpositions.

3. Hint: Separate those elements which are their own inverses and those which are not; for the latter, pair up the elements with their inverses.

Last edited by scientia (2009-11-13 11:22:36)

loida

Member

Registered: 2009-11-12

Posts: 32

Re: Algebra problem

tnx!

scientia

Member

Registered: 2009-11-13

Posts: 224

Re: Algebra problem

I'm glad I was able to help! Now that you've done your homework, you might like to check your solutions with mine.

Last edited by scientia (2009-11-14 07:19:03)

loida

Member

Registered: 2009-11-12

Posts: 32

Re: Algebra problem

wow Scientia...you don't have a clue how much I'm thankful   
actually i haven't done my homework yet(blushing), but..you made it touchable for me

i wish you the peace of God which transcends all understandings

Last edited by loida (2009-11-14 08:37:39)