A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that ...

The quotient group of N in G, written G/N and read "G modulo N", is the set of cosets of N in G. Quotient groups are also called factor groups.

17 окт. 2016 г. · Then G/N={gN:g∈G} G / N = { g N : g ∈ G } is the set of all cosets of N in G and is called the quotient group of N in G .

When N N N is a normal subgroup of a group G , G, G, the quotient group G / N G/N G/N is obtained by "collapsing the elements of N N N to the identity.

The quotient group can be simply defined as the group of cosets of a normal subgroup of a group, with respect to the composition rule of the group.

The goal of this lecture is to introduce a standard object in abstract algebra, that of quotient group. This is likely to be the most “abstract” this class will ...

The order of the quotient group is the number of distinct cosets, which is given by |G/H|=|G|/|H|, also called the index of the subgroup H⊂G.

Продолжительность: 12:37
Опубликовано: 1 апр. 2020 г.

28 дек. 2012 г. · The quotient group G/G is isomorphic to the trivial group. I write the definition for left multiplication because left cosets = right cosets. Why do we define quotient groups for normal subgroups only? Why the term and the concept of quotient group? Use of the symbol $G/N$ for the quotient group Understanding quotient groups - Mathematics Stack Exchange Другие результаты с сайта math.stackexchange.com