Definition (36). An infinite group is a group where the order/number of elements is not finite. We distinguish two main types of groups (but there are more classes out there…): 1) Discrete groups: their elements are a numerable set. Invariance … Continue reading
Schur’s lemmas are some elementary but very useful results in group theory/representation theory. They can be also used in the theory of Lie algebras so we are going to review these results in this post (for completion). FIRST SCHUR’S LEMMA. … Continue reading
Other important concepts and definitions in group theory! Definition (22). Normal or invariant group. Let be a subgroup of other group G. We say that is a normal or invariant subgroup of G if the following condition holds: Proposition. Let … Continue reading
I am going to build a “minicourse” thread on Group Theory in this and the next blog posts. I am trying to keep the notes self-contained, since group theory is a powerful tool and common weapon in the hands of … Continue reading