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Homework Statement
In S_3, show that there are four elements satisfying x^2=e and three elements satisfying y^3=e.
The Attempt at a Solution
I don't understand what the question is asking at all...
An identity element in a group is an element that, when combined with any other element in the group using the group's operation, results in that same element. In other words, it is the element that has no effect on the group's operation.
The identity element is typically denoted as "e" or "1". However, different groups may use different symbols to represent the identity element.
Yes, every group must have an identity element. This is one of the defining properties of a group. If a group does not have an identity element, it is not considered a group.
The identity element serves as the starting point for all group operations. It allows us to make connections between different elements in the group and to perform calculations more efficiently.
No, an element in a group can only have one identity element. If an element has more than one identity element, it is not considered a group.