Question

In: Advanced Math

Write the multiplication table for D8. Find the order of each element D8.

Solutions

Expert Solution

Here, denotes the identity element, is an element of order 4, and is an element of order two that isn't equal to , as in the above presentation.

The row element is multiplied on the left and the column element is multiplied on the right.

Element

Ordee of each element:

Element in terms of and	Geometric description	Order of the element
(identity element)	does nothing, i.e., leaves the square invariant	1
	rotation by angle of (i.e., ) counterclockwise	4
	rotation by angle of (i.e., ), also called a half turn	2
	rotation by angle of (i.e., ) counter-clockwise, or equivalently, by (i.e., ) clockwise	4
	reflection about the diagonal joining vertices "2" and "4"	2
	reflection about the line joining midpoints of opposite sides "14" and "23"	2
	reflection about the diagonal joining vertices "1" and "3"	2
	reflection about the line joining midpoints of opposite sides "12" and "34"	2

Colby Messinger answered 1 year ago

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