9 is a ge roup G, tl
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please answer letter d and letter e
Transcribed Image Text:For each of the following, write TRUE if the statement is always true. Otherwise, write FALSE. No need
to show solutions/proofs.
(a) If a E An, then (a) < A,.
(b) The element 9 is a generator for Z57.
(c) In a finite group G, there exists an element of order d if and only if d divides |G|.
(d) A cyclic group of order n has no proper nontrivial subgroup if and only if n is prime.
(e) If o e Sn such that o = T1 T2 · · Tk where each T; for i = 1, 2, ..., k is a transposition, then for any
positive integer n, o" = Tf'r" - . - T.
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