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Show that set of rational numbers not equal to -1 is an abelian group under a.b = a + b + ab
Автор: Prof. Sonam Kumar
Загружено: 2024-08-28
Просмотров: 3329
Описание:
A set with an operation is abelian if it is a group and the operation is commutative over the set. Conditions for a group are:
closure
associative
existence of identity
existence of inverse
In this problem, we have a set of rational numbers that are not equal to -1. It has been shown that the set has a group structure under the operation:
a.b = a + b + ab
#grouptheory @grouptheory#abeliangroup #rationalnumbers
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