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We have a semigroup (M, *), where M = R- {k} a a b = a + b-kab. Find also that, (M, *) is a group. Find the neutral element e and the inverse elements. Calculate (1-12) -1 if a - 1 is the inverse of element a.

We have a semigroup (M, *), where M = R- {k} a a b = a + b-kab. Find also that, (M, *) is a group. Find the neutral element e and the inverse elements. Calculate (1-12) -1 if a - 1 is the inverse of element a.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.7: Direct Sums (optional)
Problem 2E
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We have a semigroup (M, *), where M = R- {k} a a b = a + b-kab. Find also that, (M, *) is a group. Find the neutral element e and the inverse elements. Calculate (1-12) -1 if a - 1 is the inverse of element a.
Transcribed Image Text:We have a semigroup (M, *), where M = R- {k} a a b = a + b-kab. Find also that, (M, *) is a group. Find the neutral element e and the inverse elements. Calculate (1-12) -1 if a - 1 is the inverse of element a.
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