April 2014
Beginner to intermediate
496 pages
9h 40m
English
book
Classical Geometry: Euclidean, Transformational, Inversive, and Projective
by I. E. Leonard, J. E. Lewis, A. C. F. Liu, G. W. Tokarsky
Content preview from Classical Geometry: Euclidean, Transformational, Inversive, and Projective
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CHAPTER 10
SYMMETRY AND GROUPS
10.1 More About Groups
Recall that a set 
together with a binary operation · is called a group if the following conditions are satisfied:
1. is closed under the binary operation; that is, if x and y are elements of , then so is x · y.
is closed under the binary operation; that is, if x and y are elements of , then so is x · y.2. The associative law holds. If x, y, and z are elements of , then
, then
3. There is an identity element e in . For every x in , e · x = x · e = x.
. For every x in , e · x = x · e = x.4. is closed with respect to inversion. For every member x in , there is another member x′ also in such that x · x′ = x′ · x = e.
is closed with respect to inversion. For every member x in , there is another member x′ also in such that x · x′ = x′ · x = e.When dealing with groups in general, the binary operation ...
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