Tags » Group Theory

92: Order (Groups)

The order of a group , often denoted , is the cardinality of its underlying set. If the order is finite, then is called a finite group, and likewise for infinite order. 30 more words

Hyperoctahedral group

If you point out errors in this post, I will appreciate it.

The -cube is the subset for some . Let be the group of all symmetries of the -cube. 203 more words

Finite Group

85: The Group as a Category

The group can be viewed as equivalent to a specific kind of category, specifically the category with only a single element and all of whose morphisms are isomorphisms. 53 more words

Chinese Logic: An Introduction

Introduction

As late as 1898, logic was seen by the Chinese as “an entirely alien area of intellectual inquiry”: the sole Chinese-language textbook on logic was labeled by Liang Qichao (梁启超)—at that time a foremost authority on Western knowledge—as “impossible to classify” (无可归类), alongside museum guides and cookbooks (Kurtz, 2011: 4-5). 5,955 more words

Philosophy

The End 2016 Mathematics A To Z Roundup

As is my tradition for the end of these roundups (see Summer 2015 and then Leap Day 2016) I want to just put up a page listing the whole set of articles. 82 more words

Math

What is the use of group theory ?

When we take a ring and include division then we get a field For example, the integers Z = { … -3, -2, -1, 0, 1, 2, 3, … } form a ring, and with division we get the rational numbers… 1,439 more words

Education In Mathematics

Cosets and Lagrange's Theorem

Suppose we are given a group , a subgroup  of , and an element . We define a particular subset of , typically denoted by  in the following way: 603 more words

Group Theory