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  • Who did first use the term "simple" in group sense? More appreciated if I learn the original word(might be in French, Galois???)...

and also...

  • Why do you think that this term is chosen etymologically? A meaning of "ease"?(To me, sounds not plausible) Or, a sense of "being core/atom"?(Just a guess!)

P.S. This question might contribute a better perspective of simple groups for me and whoever reads here.

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math.stackexchange.com/questions/68220/… is related to your second question, the atom analogy is quite a good one. –  Alex J Best Jul 9 '13 at 14:23

2 Answers 2

It seems that Galois was the first to talk about simple groups using these terms. The first page of A brief history of the classification of the finite simple groups by Solomon says:

Galois introduced the concept of a normal subgroup in 1832, and Camille Jordan in the preface to his Traité des substitutions et des équations algebriques in 1870 [J1] flagged Galois’ distinction between groupes simples and groupes composées as the most important dichotomy in the theory of permutation groups.

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I don't think Galois used the term “groupes simples”, though. He seems to have just talked about proper decompositions (having a non-identity proper normal subgroup) and gave examples of non-abelian simple groups. So the term was in use by 1870 with Jordan, but I don't think it was around in 1832 with Galois. The concept certainly was with Galois, just not the word. –  Jack Schmidt Jul 9 '13 at 14:36
    
@JackSchmidt, good point. –  lhf Jul 9 '13 at 14:59

Regarding your second question, I would say the meaning is more, as you say, in the sense of being "atomic". Meaning 14a of "simple" in the Oxford English Disctionary is given as

Not composite or complex in respect of parts or structure.

This meaning has citations back to 1425 so certainly was in use whenever the sort of group was first called 'simple'. (The OED also gives the definition of "simple group" as meaning 14d, though its earliest citation is from 1888 -- Christian Felix Klein · Lectures on the ikosahedron and the solution of equations of the fifth degree, tr. by G.G. Morrice)

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