History of ElementaryGroupTheory

	Revision 7 . . February 15, 2001 1:50 am by RoseParks [*4 More Theorems]
	Revision 6 . . February 15, 2001 1:49 am by RoseParks [*Four more elementary theorems.]
	Revision 5 . . February 6, 2001 12:00 am by RoseParks
	Revision 4 . . February 5, 2001 9:40 pm by RoseParks
	Revision 3 . . February 5, 2001 10:30 am by RoseParks
	Revision 2 . . February 5, 2001 10:28 am by RoseParks
	Revision 1 . . February 5, 2001 10:24 am by RoseParks

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Difference (from prior major revision) (no other diffs)

Changed: 41c41

* If this is successful, then the assumption that the proposition is false, is, itself, false. Hence, the proposition is true.

* If this is successful, then the assumption that the proposition is false, is, itself, false. Hence, the proposition is true.

Changed: 46c46

I. For all a. b belonging to (G,*), if a*b=e, then a=b^-1 and b=a^-1.

I. For all a. b belonging to a GrouP (G,*), if a*b=e, then a=b^-1 and b=a^-1.

Changed: 62c62

II. For all a,b belonging to (G,*), (a*b)^-1=b^-1*a^-1.

II. For all a,b belonging to a GrouP (G,*), (a*b)^-1=b^-1*a^-1.

Changed: 70c70

III. For all a belonging to (G,*), (a^-1)^-1=a.

III. For all a belonging to a GrouP (G,*), (a^-1)^-1=a.

Changed: 76c76

IV. For all a,x,y, belonging to (G,*), if a*x=a*y, then x=y, and if x*a=y*a, then x=y.

IV. For all a,x,y, belonging to GrouP (G,*), if a*x=a*y, then x=y, and if x*a=y*a, then x=y.