Notes on Group Theory
نویسنده
چکیده
2 Basic group theory 2 2.1 The definition of a group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Group homomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.3 Subgroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.4 Cosets and quotient spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.5 Normal subgroups and quotient groups . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.6 The first isomorphism theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.6.1 Exact sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.7 The second isomorphism theorem (correspondence theorem) . . . . . . . . . . . . . . 8 2.8 The third isomorphism theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.9 Direct products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.10 Semidirect products (internal view) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.11 Conjugacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
منابع مشابه
Autobiographical notes
I was born in Zagreb (Croatia) on October 26, 1936. My parents were Regina (née Pavić) (April17, 1916, Zagreb–March 9, 1992, Zagreb) and Cvjetko Trinajstić (September 9, 1913, Volosko–October 29, 1998, Richmond, Australia).
متن کاملSome notes on L-projections on Fourier-Stieltjes algebras
In this paper, we investigate the relation between L-projections and conditional expectations on subalgebras of the Fourier Stieltjes algebra B(G), and we will show that compactness of G plays an important role in this relation.
متن کاملSome notes for topological centers on the duals of Banach algebras
We introduce the weak topological centers of left and right module actions and we study some of their properties. We investigate the relationship between these new concepts and the topological centers of of left and right module actions with some results in the group algebras.
متن کاملNotes on Group Theory
These are the notes prepared for the course MTH 751 to be offered to the PhD students at IIT Kanpur.
متن کاملNOTES ON REGULAR MULTIPLIER HOPF ALGEBRAS
In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition
متن کاملNotes related to the String theory and D-Branes reading group
Hopefully I will tex up notes on some of the topics that we cover during our reading group following [1]. I don’t mean to suggest that I will make exhaustive notes or even any notes on most of the discussions. However, I will try and include the important points that we discuss. Other major references were [2, 3] and my notes from [4]. A more technical discussion of the BRST quantisation of a g...
متن کامل