9.3: Reading Questions

Abstract Algebra: Theory and Applications · LibreTexts

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    From LibreTexts, under GNU Free Documentation, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    1

    Determine the order of \((1,2)\) in \({\mathbb Z_4}\times{\mathbb Z_8}\text{.}\)

    2

    List three properties of a group that are preserved by an isomorphism.

    3

    Find a group isomorphic to \(\mathbb Z_{15}\) that is an external direct product of two non-trivial groups.

    4

    Explain why we can now say “the infinite cyclic group”?

    5

    Compare and contrast external direct products and internal direct products.

    This page titled 9.3: Reading Questions was last modified on Tue, 01 Sep 2026 06:45:26 GMT and is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Thomas W. Judson (Abstract Algebra: Theory and Applications) via source content that was edited to the style and standards of the LibreTexts platform.