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**hkhk**

if G= Z4 x Z what would be the torsion group T(G)?

and what is the factor group of G/ T(G) ?

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- Thread starter hkhk
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- #1

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if G= Z4 x Z what would be the torsion group T(G)?

and what is the factor group of G/ T(G) ?

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- #2

quasar987

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What have you tried?

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the cyclic group <(1,0)> is the torsion group

( (0,0) (1,0) (2,0) (3,0))

?

( (0,0) (1,0) (2,0) (3,0))

?

- #4

quasar987

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Do you know any group in which every element has finite order? If so, that will be a torsion group.

Do you know any group in which no element other than the identity has finite order? If so, that will be a torsion free group.

- #5

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1. then Q is a torsion free abelian group . true?

2. i was trying to find a set of elements of G= Z4 x Z that has finite order

2. i was trying to find a set of elements of G= Z4 x Z that has finite order

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- #6

quasar987

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What do these i) and ii) refer to?

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i edited the question

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quasar987

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- #9

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Z4 is a group of finite order

and Z is not

so Z4 is a torsion group, while Z is torsion free, am i on the right track

sorry i do not have a very strong background in this topic and i am teaching myself this so that i can understand more advanced math

thanks a lot for your help

and Z is not

so Z4 is a torsion group, while Z is torsion free, am i on the right track

sorry i do not have a very strong background in this topic and i am teaching myself this so that i can understand more advanced math

thanks a lot for your help

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- #10

quasar987

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As for the second question, what have you tried and where are you stuck?

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