fix: proofread More on Groups part - #321
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- action.tex: fix missing period and missing cardinality bars around |O| in the normal-subgroup-of-prime-index hint - sylow.tex: fix typo "there is at exactly one" -> "there is exactly one" - structure.tex: fix index mismatch e_1 -> e_i in the dimension formula of the primary-form uniqueness proof, and s -> s_1 in Smith normal form proof Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016HZdCN5NoxqtbdrD3gZeGi
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Proofreading of the More on Groups part (issue #315), covering the chapters:
tex/H113/action.tex(Group actions overkill AIME problems)tex/H113/sylow.tex(Find all groups)tex/H113/structure.tex(The PID structure theorem)Fixes
All issues found were minor (typos / notation slips):
action.tex— In the hint for the "subgroup of smallest-prime index is normal" problem: added a missing period after "Consider any orbitsylow.tex— In the solution showing no simple group of order 56 exists: "there is at exactly one Sylowstructure.tex— In the primary-form uniqueness proof, fixed an index mismatch in the dimension formula: "$R/(p^{e_1})$" → "$R/(p^{e_i})$" (the summand index should beI verified the worked computations along the way (the AIME/Burnside count of$300$ , the triple-product-of-primes element count, the Smith normal form Euclidean-algorithm example, and the $\mathbb{Z}/9 \oplus \mathbb{Z}/3^5$ quotient-dimension example); all check out. No large mathematical errors were found.
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