Would it be possible to infer that [itex]b^5 = e[/itex] (where [itex]e[/itex] is the group's identity element) from(adsbygoogle = window.adsbygoogle || []).push({});

[tex]b^{5} a = ab^{5} [/tex]

given that [itex]a^{2}=e[/itex]?

(Basically we are given [itex]b^{2}a=ab^{3}[/itex] and [itex]a^{2}=e[/itex] and asked to show that [itex]b^{5}=e[/itex], though I've managed to infer the "equation" above and I can't quite see how we'd move to inferring what is needed. Maybe it's either very simple and I'm missing it or there's a bit of reasoning that I need.)

Thanks.

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# Homework Help: Groups: b^5a = ab^5

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