Hyperoperations Wiki - User contributions [en]

User:Natsugou

2026-06-26T20:39:02Z

Natsugou: Created page with "This is Natsugou's personal page. English works: Negative rank hyperoperations (2023) https://googology.fandom.com/wiki/User_blog:Natsugoh/Negative_rank_hyperoperations Sol..."

This is Natsugou's personal page.

English works:

Negative rank hyperoperations (2023)
https://googology.fandom.com/wiki/User_blog:Natsugoh/Negative_rank_hyperoperations

Solving the functional equation a◦f = g◦a for f and for g (2024)
https://googology.fandom.com/wiki/User_blog:Natsugoh/Solving_the_functional_equation_a%E2%97%A6f_%3D_g%E2%97%A6a_for_f_and_for_g

Discriminating whether a function of a real variable is an iterated function (2024)
https://googology.fandom.com/wiki/User_blog:Natsugoh/Discriminating_whether_a_function_of_a_real_variable_is_an_iterated_function

A fee subgroup is not necessarily normal (2025)
https://googology.fandom.com/wiki/User_blog:Natsugoh/A_fee_subgroup_is_not_necessarily_normal

Japanese works:

ハイパー演算の整数拡張 (Negative rank hyperoperations) (2022)
https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Natsugoh/%E3%83%8F%E3%82%A4%E3%83%91%E3%83%BC%E6%BC%94%E7%AE%97%E3%81%AE%E6%95%B4%E6%95%B0%E6%8B%A1%E5%BC%B5

ハイパー演算の整数拡張改訂 (Negative rank hyperoperations revision) (2023)
https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Natsugoh/%E3%83%8F%E3%82%A4%E3%83%91%E3%83%BC%E6%BC%94%E7%AE%97%E3%81%AE%E6%95%B4%E6%95%B0%E6%8B%A1%E5%BC%B5_%E6%94%B9%E8%A8%82

関数方程式a◦g=f◦aをfについて, およびgについて解く (Solving the functional equation a◦f = g◦a for f and for g) (2024)
https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Natsugoh/%E9%96%A2%E6%95%B0%E6%96%B9%E7%A8%8B%E5%BC%8Fa%E2%97%A6g%3Df%E2%97%A6a%E3%82%92f%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6,_%E3%81%8A%E3%82%88%E3%81%B3g%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A7%A3%E3%81%8F

実変数関数を写像の反復か否か判定 (Discriminating whether a function of a real variable is an iterated function) (2024)
https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Natsugoh/%E5%AE%9F%E5%A4%89%E6%95%B0%E9%96%A2%E6%95%B0%E3%82%92%E5%86%99%E5%83%8F%E3%81%AE%E5%8F%8D%E5%BE%A9%E3%81%8B%E5%90%A6%E3%81%8B%E5%88%A4%E5%AE%9A

フィーは必ずしも正規でない (A fee subgroup is not necessarily normal) (2025)
https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Natsugoh/%E3%83%95%E3%82%A3%E3%83%BC%E3%81%AF%E5%BF%85%E3%81%9A%E3%81%97%E3%82%82%E6%AD%A3%E8%A6%8F%E3%81%A7%E3%81%AA%E3%81%84

可換な全順序群の全ての正元からなる半群(正錐)からの準同型の分類 (work in progress)
https://drive.google.com/file/d/1PQfcqGvQKIRt8EXaWAsIrPjM2A9UJTmX/view?usp=sharing

Fee subgroup

2025-11-08T14:50:09Z

Natsugou:

A fee subgroup \(H\) of a linearly ordered subgroup \(G\)is a subgroup such that \(g^{-1}Hg \subset H\) for all \(g > 1\).

When a map \(a\) defined on a linearly ordered group \(G\) satisfies that \(a(g) = a(h)\) implies \(a(fg) = a(fh)\) for all \(f > 1\),
\(P(a) = \{g^{-1}h \mid a(g) = a(h)\}\) is a fee subgroup<ref name="a">https://tetrationforum.org/showthread.php?tid=1812&pid=12309#pid12309</ref>.

A fee subgroup is not always normal <ref name="b">https://googology.fandom.com/wiki/User_blog:Natsugoh/A_fee_subgroup_is_not_necessarily_normal</ref>.

<references />

Fee subgroup

2025-11-08T14:49:11Z

Natsugou:

A fee subgroup \(H\) of a linearly ordered subgroup \(G\)is a subgroup such that \(g^{-1}Hg \subset H\) for all \(g > 1\).

When a map \(a\) defined on a linearly ordered group \(G\) satisfies that \(a(g) = a(h)\) implies \(a(fg) = a(fh)\),
\(P(a) = \{g^{-1}h \mid a(g) = a(h)\}\) is a fee subgroup<ref name="a">https://tetrationforum.org/showthread.php?tid=1812&pid=12309#pid12309</ref>.

A fee subgroup is not always normal <ref name="b">https://googology.fandom.com/wiki/User_blog:Natsugoh/A_fee_subgroup_is_not_necessarily_normal</ref>.

<references />

Fee subgroup

2025-11-08T14:47:35Z

Natsugou:

A fee subgroup \(H\) of a linearly ordered subgroup \(G\)is a subgroup such that \(g^{-1}Hg \subset H\) for all \(g > 1\).

When \(G\) is linearly ordered and \(a(g) = a(h)\) implies \(a(fg) = a(fh)\),
\(P(a) = \{g^{-1}h \mid a(g) = a(h)\}\) is a fee subgroup<ref name="a">https://tetrationforum.org/showthread.php?tid=1812&pid=12309#pid12309</ref>.

A fee subgroup is not always normal <ref name="b">https://googology.fandom.com/wiki/User_blog:Natsugoh/A_fee_subgroup_is_not_necessarily_normal</ref>.

<references />

Fee subgroup

2025-11-08T13:19:43Z

Natsugou:

A fee subgroup \(H\) of a linearly ordered subgroup \(G\)is a subgroup such that \(g^{-1}Hg \subset H\) for all \(g > 1\).

When \(G\) is linearly ordered, and \(a(g) = a(h)\) implies \(a(fg) = a(fh)\) and \(a(gf) = a(hf)\) for all \(f > 1\),
or when \(G\) is bi-ordered, and \(a(g) = a(h)\) implies \(a(fg) = a(fh)\) for all \(f > 1\),
\(P(a) = \{g^{-1}h \mid a(g) = a(h)\}\) is a fee subgroup<ref name="a">https://tetrationforum.org/showthread.php?tid=1812&pid=12309#pid12309</ref>.

A fee subgroup is not always normal <ref name="b">https://googology.fandom.com/wiki/User_blog:Natsugoh/A_fee_subgroup_is_not_necessarily_normal</ref>.

<references />

Fee subgroup

2025-09-21T09:52:45Z

Natsugou:

A fee subgroup \(H\) of a linearly ordered subgroup \(G\)is a subgroup such that \(g^{-1}Hg \subset H\) for all \(g > 1\).

When \(G\) is bi-ordered, and \(a(g) = a(h)\) implies \(a(fg) = a(fh)\) and \(a(gf) = a(hf)\) for all \(f > 1\),
\(P(a) = \{g^{-1}h \mid a(g) = a(h)\}\) is a fee subgroup<ref name="a">https://googology.fandom.com/wiki/User_blog:Natsugoh/Discriminating_whether_a_function_of_a_real_variable_is_an_iterated_function</ref>.

A fee subgroup is not always normal <ref name="b">https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Natsugoh/%E3%83%95%E3%82%A3%E3%83%BC%E3%81%AF%E5%BF%85%E3%81%9A%E3%81%97%E3%82%82%E6%AD%A3%E8%A6%8F%E3%81%A7%E3%81%AA%E3%81%84</ref>.

<references />

Fee subgroup

2025-09-20T11:44:37Z

Natsugou:

A fee subgroup \(H\) of a linearly ordered subgroup \(G\)is a subgroup such that \(g^{-1}Hg \subset H\) for all \(g > 1\).

When \(a(g) = a(h)\) implies \(a(fg) = a(fh)\) and \(a(gf) = a(hf)\) for all \(f > 1\),
\(P(a) = \{g^{-1}h \mid a(g) = a(h)\}\) is a fee subgroup<ref name="a">https://googology.fandom.com/wiki/User_blog:Natsugoh/Discriminating_whether_a_function_of_a_real_variable_is_an_iterated_function</ref>.

A fee subgroup is not always normal <ref name="b">https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Natsugoh/%E3%83%95%E3%82%A3%E3%83%BC%E3%81%AF%E5%BF%85%E3%81%9A%E3%81%97%E3%82%82%E6%AD%A3%E8%A6%8F%E3%81%A7%E3%81%AA%E3%81%84</ref>.

<references />

Fee subgroup

2025-09-20T11:43:21Z

Natsugou: Created page with "A fee subgroup \(H\) of a linearly ordered subgroup \(G\)is a subgroup such that \(g^{-1}Hg \subset H\) for all \(g > 1\). When \(a(g) = a(h)\) implies \(a(fg) = a(fh)\) and..."

A fee subgroup \(H\) of a linearly ordered subgroup \(G\)is a subgroup such that \(g^{-1}Hg \subset H\) for all \(g > 1\).

When \(a(g) = a(h)\) implies \(a(fg) = a(fh)\) and \(a(gf) = a(hf)\) for all \(f > 1\),
\(P(a) = \{g^{-1}h \mid a(g) = a(h)\}\) is a fee subgroup<ref name="a">https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Natsugoh/%E5%AE%9F%E5%A4%89%E6%95%B0%E9%96%A2%E6%95%B0%E3%82%92%E5%86%99%E5%83%8F%E3%81%AE%E5%8F%8D%E5%BE%A9%E3%81%8B%E5%90%A6%E3%81%8B%E5%88%A4%E5%AE%9A</ref>.

A fee subgroup is not always normal <ref name="b">https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Natsugoh/%E3%83%95%E3%82%A3%E3%83%BC%E3%81%AF%E5%BF%85%E3%81%9A%E3%81%97%E3%82%82%E6%AD%A3%E8%A6%8F%E3%81%A7%E3%81%AA%E3%81%84</ref>.

<references />