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fix: proofread More on Groups part - #321

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claude/loving-clarke-57oqrg
Jun 24, 2026
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fix: proofread More on Groups part#321
vEnhance merged 1 commit into
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claude/loving-clarke-57oqrg

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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 orbit $\mathcal O$", and restored the missing cardinality bars in "so $\mathcal O$ divides $n$" → "so $|\mathcal O|$ divides $n$".
  • sylow.tex — In the solution showing no simple group of order 56 exists: "there is at exactly one Sylow $2$-subgroup" → "there is exactly one Sylow $2$-subgroup".
  • structure.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 be $i$, not $1$; the surrounding numerator already used $e_i$). Also in the Smith normal form proof, "$s$" → "$s_1$" to match the variable defined just above.

I 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.

🤖 Generated with Claude Code


Generated by Claude Code

- 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
@vEnhance vEnhance added the proofreading-campaign Systematic full proofreading of text label Jun 24, 2026 — with Claude
@vEnhance vEnhance mentioned this pull request Jun 24, 2026
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vEnhance merged commit 9dcc56d into main Jun 24, 2026
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