- #1
ilyas.h
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Homework Statement
Homework Equations
subgroup axioms:
1. a, b in T(G), then ab in T(G)
2. existence of identity element.
3. a in T(G), then a^-1 in T(G)
The Attempt at a Solution
1.
let a be in T(G), then a^n = e.
let b be in T(G), then b^n = e
(ab)^n = (a^n)(b^n) = (e)(e) = e
axiom 1 holds.
2.
let e be in T(G), then e^n = e
conclusion: identity element, e, of G, must be 1.
3.
let a be in T(G), then a^n = e.
show that (a^-1)^n = e
(a^-1)^n = (a^n)^-1 = 1 / a^n = 1 / e
therefore
(a^-1)^n = 1 / e
we know from axiom 2 that e = 1, so:
1 / e = e.
Done.
Is my proof correct? there's not markscheme, can't check answer,