Theorem 2.3.1: Let (G, o) be a group, a e G, and m, n e N, then the powe the following laws of exponents: (a) a" o am = an+m = amoa", (a"ym= anm%3D a= (a")-1, (d) e = e. (amy", (c) %D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Proof that
Theorem 2.3.1: Let (G, o) be a group, ae G, and m,ne N, then the powers of a satisfy
the following laws of exponents:
(a) a" o am an+m = a"oa",
(b) (a"yn = anm=
(a")-1,
(d) e = e.
(am)",
(c) a =
Transcribed Image Text:Theorem 2.3.1: Let (G, o) be a group, ae G, and m,ne N, then the powers of a satisfy the following laws of exponents: (a) a" o am an+m = a"oa", (b) (a"yn = anm= (a")-1, (d) e = e. (am)", (c) a =
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