課程名稱︰代數導論一
課程性質︰系定必修
課程教師︰黃漢水 教授
開課系所︰數學系
考試時間︰2006/10/02 10:20-11:20
是否需發放獎勵金：否
一 Let G be a group, a,b,c∈G and suppose that (a*b)*c=e (35%)
(1)prove or disprove that (b*c)*a=e
(2)prove or disprove that (c*b)*a=e
二 Let Q be the set of all rational numbers, S={a∈Q│a≠0},
T={a∈Q│a≠1} and φ:S→T be a funtion defined by φ(a)=3a+1
for a∈S. (35%)
We know that S is a group with respect to multiplication.
Give the definition of a binary operation * on T such that T is a group
and φ is an isomorphism.
三 Let G be a group and,│G│=3 and suppose that G={e,a,b}.(30%)
(1)prove that a*b=e
(2)prove that a^2=b and a^3=e
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