# Cyclic groups

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(a) Let F = { (matrix with first row; a 0, second row is 0 a) : a is an element of R

Show that F is a field and that F ~= R

(b) Give the definition of a cyclic group

Prove that every subgroup H of a cyclic group G =<a> is itself cyclic

https://brainmass.com/math/basic-algebra/cyclic-groups-modern-algebra-3692

#### Solution Summary

This is a proof regarding fields. The cyclic groups for modern algebra are examined.

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