Subgroup and Cosets of Subgroups

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III-24.C1.

Summary.

We introduce notion of subgroup, coset of a subgroup, sets of left and right cosets of a subgroup. We define multiplication of two subset of a group, subset of reverse elemens of a group, intersection of two subgroups. We define the notion of an index of a subgroup and prove Lagrange theorem which states that in a finite group the order of the group equals the order of a subgroup multiplied by the index of the subgroup. Some theorems that belong rather to [1] are proved.

MML Identifier: GROUP_2

Contents (PDF format)

Bibliography

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