# Thread:

1. ## Automorphism of a subgroup of an abelian group

Let $A \cong C_n^{m}$ be an abelian group consisting of the direct product of $C_n$ $m$-times for $m \in \mathbb{N} \cup \{\infty\}$. Let $H \leq A$.

My question is this: if $\phi$ is an automorphism of $H$ then does $\phi$ extend to an automorphism of $A$? If not in general, what if $n$ is prime?
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8083115220069885, "perplexity_flag": "head"}