Which of the following statements are True, and which are False ? Give reasons for your answers. (a) There is a finite field of order 45. (b) A group G of order 9 has a representation of order 2. (c) Every free abelian group is a free group.
Which of the following statements are True, and which are False ? Give reasons for your answers. (a) There is a finite field of order 45. (b) A group G of order 9 has a representation of order 2. (c) Every free abelian group is a free group.
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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Transcribed Image Text:1.
Which of the following statements are True, and
which are False ? Give reasons for your answers.
(a)
There is a finite field of order 45.
(b)
A group G of order 9 has a representation
of order 2.
(c)
Every free abelian group is a free group.
(d).
Every set is a semi-group.
(e)
If G is an infinite group acting on an
infinite set X, then no element of X has
finite stabiliser.
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