Cyclic Subgroup H=<9> of Z30: List and Find Elements

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Homework Help Overview

The discussion revolves around identifying elements of a cyclic subgroup H=<9> within the additive group Z30. Participants are exploring the structure and elements of this subgroup.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to list the elements of the subgroup H=<9> and are questioning the correctness of their initial assumptions. There is also a request for clarification on the meaning of part (b) of the problem.

Discussion Status

The discussion is ongoing, with some participants providing corrections and additional insights regarding the elements of the subgroup. There is an exploration of how to generate the subgroup from its elements.

Contextual Notes

Participants are working under the constraints of additive group properties and are questioning the implications of those properties on the subgroup's elements.

tasha10
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1. (a) List all elements in H=<9>, viewed as a cyclic subgroup of Z30
(b) Find all z in H such that H=<z>





I'm thinking that H=<9> = {1,7,9} (viewed as a cyclic subgroup of Z30) is this correct?
And could someone explain what (b) is asking in other terms?
 
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tasha10 said:
I'm thinking that H=<9> = {1,7,9} (viewed as a cyclic subgroup of Z30) is this correct?
And could someone explain what (b) is asking in other terms?

No that is not correct. Z30 is an additive group so H=<9> contains 9, 9+9, 9+9+9 etc.

Part (b) asks which elements of H could produce H by just adding it to itself repeatedly
 
so {9,18,27}?
 
No, quite a few more. What do you get if you add 9 to 27 in Z30?
 

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