(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A is a subset of R and G is a set of permutations of A. Show that G is a subgroup of S_A (the group of all permutations of A). Write the table of G.

Onto the actual problem:

A is the set of all nonzero real numbers.

[itex]G={e,f,g,h}[/itex]

where e is the identity element, f(x) = 1/x, g(x) = -x, h(x) = -1/x

Would this be the right way to do it?

For each combination of elements in G (call the elements a,b) I need to show

a*b is in G

I also need to show that the inverse of a is in G.

Here is where I get confused, I'll start with with a = e:

ee = e

ef = f

eg = g

eh = h

Okay, that is all good, now letting a = f:

fe = e

ff = e

fg = h

fh = g

now a = g:

ge = g !

gf = h

gg = g !

gh = e

now a = h:

he = h

hf = g !

hg = f

hh = g !

What am I doing wrong here?

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# Homework Help: Abstract Algebra - Subgroup of Permutations

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