MA 45300 Lecture Notes - Lecture 42: Homomorphism, Normal Subgroup

• School: Purdue University
• Department: Mathematics
• Course: MA 45300
• Professor: All

Document Summary

Bijective homomorphism, or in other words the exact same thing. We can transform certain functions albeit it not perfectly. If there is a function that transforms g onto h, we call that a homomorphic image of g. this is known as a homomorphism form tog. h into is a homomorphism if are groups, then. If there is a homomorphism from onto. Let"s consider the example of adding even and odd elements. After repeating this for all 4, we find that this is a homomorphism under addition. f : g h (e) (a ) Consider (ee) (a)f(a ) f (a multiplicative inverse of. 1 f f (a (a), (e) & f(ee) 1 f (e)f(e) f (e), (e)f(e) (a)f(a ) (e) X f : g h x x 1. Eg: 1 = . G has a conjugacy if it"s of the. This is quite similar to the definition of conjugate. > & a f : g h.