Let G be the multiplicative group of all nonsingular 2 X 2 matrices with rational entries. Show
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Let G be the multiplicative group of all nonsingular 2 X 2 matrices with rational entries. Show that a=has order 4 and b =has order 3, but ab has infinite order. Conversely, show that the additive groupZ2⊕Z contains nonzero elements a,b of infinite order such that a + b has finite order.
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To show that a has order 4 we first compute a2 and a4 Since a4 is the identit...View the full answer
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Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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