View source for Tour:Left coset of a subgroup

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{{derivative of|left coset of a subgroup}}
{{tour-regular|
target = beginners|
secnum = three|
next = Left cosets partition a group|
previous = Union of two subgroups is not a subgroup}}
{{quotation|'''PREREQUISITES''': Definition of group and subgroup, notations typically used for multiplying elements and subsets, and the techniques for manipulating equations in groups. Review [[Tour:Manipulating equations in groups]] and [[Tour:Mind's eye test two#Manipulating equations for subsets and their products]]<br>'''WHAT YOU NEED TO DO''':
* Read the equivalent definitions of left coset given below.
* Prove to yourself that they're equivalent (there's a link to a page explaining the equivalence, but try this on your own). If you find this hard, review the suggested prerequisites pages.}}
{{#lst:Left coset of a subgroup|beginner}}
{{quotation|'''WHAT'S MORE''': Stated below are more examples and further facts about left cosets. We'll be seeing some of these facts very soon, while others will be seen much later. Go through the list of facts, and ignore those that seem hard to comprehend.}}
{{#lst:Left coset of a subgroup|revisit}}
{{tour-regular-bottom|
target = beginners|
secnum = three|
next = Left cosets partition a group|
previous = Union of two subgroups is not a subgroup}}