User:Lériendil/Square and triangle superparticulars by prime subgroup: Difference between revisions
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Some shorthand notation used here: | Some shorthand notation used here: | ||
* S''k'' stands for ''k''^2/[(''k''-1)(''k''+1)] by standard convention. | * S''k'' stands for ''k''^2/[(''k''-1)(''k''+1)] by standard convention (the ''k''th square superparticular). | ||
* T''k'' = S''k'' * S(''k''+1) stands for [''k''(''k''+1)/2]/[(''k''-1)(''k''+2)/2]. | * T''k'' = S''k'' * S(''k''+1) stands for [''k''(''k''+1)/2]/[(''k''-1)(''k''+2)/2] (the ''k''th triangle superparticular). | ||
* U''k'' = S''k''/S(''k''+1) stands for the ''k''th ultraparticular, which has the same subgroup as T''k'' except in the case where k is congruent to 4 (mod 9), in which case the subgroup of U''k'' lacks prime 3 from that of T''k''. | |||
* L''p'' refers to the ''p''-limit, i.e. the subgroup of primes less than or equal to ''p''. | * L''p'' refers to the ''p''-limit, i.e. the subgroup of primes less than or equal to ''p''. | ||
* L''p''(-''q'') refers to the ''p'' limit with the prime ''q'' omitted: e.g. L17(-11) refers to the 2.3.5.7.13.17 subgroup; these omissions can be stacked so that L23(-5.17) refers to the group 2.3.7.11.13.19.23. | * L''p''(-''q'') refers to the ''p'' limit with the prime ''q'' omitted: e.g. L17(-11) refers to the 2.3.5.7.13.17 subgroup; these omissions can be stacked so that L23(-5.17) refers to the group 2.3.7.11.13.19.23. | ||
This list eventually aims to be complete to the | This list eventually aims to be complete to the 29-add-one-limit, i.e. the class of subgroups with at most one prime greater than 29, which is a superset of the 31-limit. | ||
== 2- and 3-prime subgroups (2.3 and 2.3.p) == | == 2- and 3-prime subgroups (2.3 and 2.3.p) == | ||
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| [[15/14]] | | [[15/14]] | ||
| {{monzo| -1 1 1 -1 }} | | {{monzo| -1 1 1 -1 }} | ||
|- | |||
| T6 | |||
| [[7-limit|L7]] | |||
| [[21/20]] | |||
| {{monzo| -2 1 -1 1 }} | |||
|- | |||
| T8 | |||
| [[7-limit|L7]] | |||
| [[21/20]] | |||
| {{monzo| -2 1 -1 1 }} | |||
|- | |- | ||
| T9 | | T9 | ||