Tour:Left coset of a subgroup

This article adapts material from the main article: left coset of a subgroup

This page is part of the Groupprops Guided tour for beginners (Jump to beginning of tour)
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PREREQUISITES: Definition of group and subgroup, notations typically used for multiplying elements and subsets.
WHAT YOU NEED TO DO:

• Read the equivalent definitions of left coset given below.
• Try to see why they're equivalent (there's a link to a page explaining the equivalence, but it's a good exercise to check this).
• Quickly go through the various facts stated about left cosets. We'll be encountering some of them in the coming pages.
• Convince yourself of the fact that the left cosets of a subgroup are pairwise disjoint, and hence form a partition of the group (this is clear from some of the equivalent formulations of the definition).

This page is part of the Groupprops Guided tour for beginners (Jump to beginning of tour). If you found anything difficult or unclear, make a note of it; it is likely to be resolved by the end of the tour.
PREVIOUS: Union of two subgroups is not a subgroup | UP: Introduction three (beginners) | NEXT: Left cosets are in bijection via left multiplication