# Groups and elements

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If G is a group of order p^k, where p is a prime and k >=, show that G must have an element of order p.

Â© BrainMass Inc. brainmass.com March 6, 2023, 1:19 pm ad1c9bdddfhttps://brainmass.com/math/group-theory/groups-elements-15177

#### Solution Preview

Proof:

If k=1, the result holds obviously.

Suppose the result holds for all t less than k, now for |G|=p^k,

Consider an element g in ...

#### Solution Summary

This is a proof of prime groups and elements with given order.

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