Soluble Groups in Algebra: What Are They and What Branch Do They Fall Under?

[pivoxa15]

How does soluble groups fit into algebra? Why is there another name for it called solvable groups?

What branch does it fall under?

 

[Kummer]

Maybe "solvable" is American and "soluble" is English. For example, "formula" is American and "formulae" is English. Look at the author's name of the book, is it English?

 

[pivoxa15]

That is hard to swallow. I've only heard soluble made reference as a chemistry term.

 

[matt grime]

Formula is latin, and is the same in both English and American English. Formulae is the 'proper' plural in both languages too, though formulas is now acceptable in either.

 

[JasonRox]

That is hard to swallow. I've only heard soluble made reference as a chemistry term.

How is this hard to swallow?

It's as easy as... English book means its solvable.

 

[Kummer]

Do you agree with me it is just a difference in language?

 

[quasar987]

I suppose solvable groups get their name from the results of Galois, "The general polynomial equation of degree n is solvable by radicals if and only if S_n (the symmetric group) is solvable".

(Together with the trivial observation that "S_n is solvable if and only if n is inferior to 5", this constitute an argument of the unsolvability of general polynomial equations of degree >4 by radiacals)

 

[pivoxa15]

Do you agree with me it is just a difference in language?

From this entry, maybe I do.

http://en.wiktionary.org/wiki/soluble

 

[quasar987]

Especially since Galois was french!

 

[matheinste]

Hello all.

The Oxford English Dictionary which purports to give the first written use of all words in the English language has an entry for soluble:

Soluble (Math)=solvable. Giving its first recorded use in this sense as being in the 1902 edition of the Encyclopedia Britannica. The quote is:-

''A group defines uniquely the set of factor-groups that occur in its composition series ...When the order of all the factor groups are primes the group is said to be soluble.''

It also gives the first recorded use of the word solvable in the mathematical sense as being in 1892 by E.Netto in His Theory of Substitutions.

I hope this is of some use.

Matheinste.

Matheinste.