Thread: Michael Artin's Algebra

I'm taking an algebra course and was told to purchase Dummit and Foote's Abstract Algebra, but when I showed up for class I found out that we were using Artin's Algebra. I have obtained a copy of the homework problems, but one of them asks us to do something with formulas (1.6) and (6.15) from Chapter 2. Could anyone who owns this book tell me what those two formulae are?

Thanks.

Originally Posted by redsoxfan325

I'm taking an algebra course and was told to purchase Dummit and Foote's Abstract Algebra, but when I showed up for class I found out that we were using Artin's Algebra. I have obtained a copy of the homework problems, but one of them asks us to do something with formulas (1.6) and (6.15) from Chapter 2. Could anyone who owns this book tell me what those two formulae are?

Thanks.

Question (1.6): Wrirte out all ways in which one can form a product of four elements a,b,c,d in the given order.

Question (6.5): Justify (6.15) carefully

(6.15) is: et f: G --: G' be a homomorphism of finite groups, then |G| = |ker F||Im F|.
Thus |ker F| divides |G| and |Im F| both |G| and |G'|.

Tonio

Pd. You better get a copy of Artin's book in the school's library ...or in gigapedia.org.

Originally Posted by tonio

Question (1.6): Wrirte out all ways in which one can form a product of four elements a,b,c,d in the given order.

Question (6.5): Justify (6.15) carefully

(6.15) is: et f: G --: G' be a homomorphism of finite groups, then |G| = |ker F||Im F|.
Thus |ker F| divides |G| and |Im F| both |G| and |G'|.

Tonio

Pd. You better get a copy of Artin's book in the school's library ...or in gigapedia.org.

Thanks. I was looking for the formulae though, not the actual problems. There should be a formula labeled 1.6 in Chapter 2 Section 1 somewhere that should have something to do with finite groups (probably). Thank you for the (6.15) formula.

Originally Posted by redsoxfan325

Thanks. I was looking for the formulae though, not the actual problems. There should be a formula labeled 1.6 in Chapter 2 Section 1 somewhere that should have something to do with finite groups (probably). Thank you for the (6.15) formula.

Formula (1.6): (ab)' = b'a' , with x' = x^(-1).

Tonio