Matches in SemOpenAlex for { <https://semopenalex.org/work/W1525491230> ?p ?o ?g. }
Showing items 1 to 55 of
55
with 100 items per page.
- W1525491230 abstract "As an abstract group, the (2,3,n) triangle group has the presentation mit _n = This thesis is concerned with subgroups of finite index in mit 9, mit _11 and mit 13. With a subgroup of finite index, u, in the (2,3,11) triangle group, we associate a quintuple of non-negative integers (u,p,e,f,g), with u 1 and 5u = 132(p - 1) + 33e + 44f + 60g. We show in Theorem 1.4.6 that each quintuple, satisfying the conditions, corresponds to a subgroup of mit 11. With a subgroup of finite index, u, in the (2,3,12) triangle group, we associate a quintuple of non-negative integers (u,p,e,f,g), with u 1 and 7u = 156(p - 1) + 39e + 52f + 72g. We show in Theorem 3.3.6 that each quintuple, satisfying the conditions, corresponds to a subgroup of mit 13. With a subgroup of finite index, u, in the (2,3,9) triangle group, we associate a sextuple of non-negative integers (u,p,e,f,g1,g3) with u 1, u = f (mod 3) and u = 36(p - 1) + 9e + 12f + 16g_1 + 12g_3. We show in Theorem 2,3,9 that each sextuple, satisfying the conditions, corresponds to a subgroup of mit 9 with the following exceptions: (a) (12n+ 9,0,1,0,0,n+ 3), V n 0 (b) (24,0,0,0,0,5) (c) (24,0,0,0,3,1) (d) (24,0,0,3,0,2) Coset diagrams are used extensively in the proofs, although to prove exception (a) for mit 9, we make use of Hauptmodul equations (see [1] and [23]). Computer programs were developed to generate all quintuples satisfying the relevant conditions for (2,3,110 subgroups for u 101, all quintuples satisfying the relevant conditions for (2,3,13) subgroups for u 110, and all sextuples satisfying the relevant conditions for (2,3,9) subgroups for u 38. These programs and their output are presented in the Appendices. We show in Theorem 1.2.2 that quintuples, which satisfy the relevant (2,3,11) conditions, exist for each u 99. We show in Theorem 2.2.1 that sextuples, which satisfy the relevant (2,3,9) conditions, exist for each u 36. We show in Theorem 3.2.1 that quintuples, which satisfy the relevant (2,3,13) conditions, exist for each u 104." @default.
- W1525491230 created "2016-06-24" @default.
- W1525491230 creator A5028539563 @default.
- W1525491230 date "1992-01-01" @default.
- W1525491230 modified "2023-09-28" @default.
- W1525491230 title "Subgroups of some (2, 3, n) triangle groups" @default.
- W1525491230 hasPublicationYear "1992" @default.
- W1525491230 type Work @default.
- W1525491230 sameAs 1525491230 @default.
- W1525491230 citedByCount "0" @default.
- W1525491230 crossrefType "dissertation" @default.
- W1525491230 hasAuthorship W1525491230A5028539563 @default.
- W1525491230 hasConcept C105515060 @default.
- W1525491230 hasConcept C114614502 @default.
- W1525491230 hasConcept C121332964 @default.
- W1525491230 hasConcept C2777404646 @default.
- W1525491230 hasConcept C2781311116 @default.
- W1525491230 hasConcept C33923547 @default.
- W1525491230 hasConcept C62520636 @default.
- W1525491230 hasConcept C85307737 @default.
- W1525491230 hasConceptScore W1525491230C105515060 @default.
- W1525491230 hasConceptScore W1525491230C114614502 @default.
- W1525491230 hasConceptScore W1525491230C121332964 @default.
- W1525491230 hasConceptScore W1525491230C2777404646 @default.
- W1525491230 hasConceptScore W1525491230C2781311116 @default.
- W1525491230 hasConceptScore W1525491230C33923547 @default.
- W1525491230 hasConceptScore W1525491230C62520636 @default.
- W1525491230 hasConceptScore W1525491230C85307737 @default.
- W1525491230 hasLocation W15254912301 @default.
- W1525491230 hasOpenAccess W1525491230 @default.
- W1525491230 hasPrimaryLocation W15254912301 @default.
- W1525491230 hasRelatedWork W1975311321 @default.
- W1525491230 hasRelatedWork W1980446010 @default.
- W1525491230 hasRelatedWork W1984886700 @default.
- W1525491230 hasRelatedWork W1994125001 @default.
- W1525491230 hasRelatedWork W2012076818 @default.
- W1525491230 hasRelatedWork W2021007909 @default.
- W1525491230 hasRelatedWork W2027345217 @default.
- W1525491230 hasRelatedWork W2030444635 @default.
- W1525491230 hasRelatedWork W2041060051 @default.
- W1525491230 hasRelatedWork W2051742383 @default.
- W1525491230 hasRelatedWork W2057781751 @default.
- W1525491230 hasRelatedWork W2061693646 @default.
- W1525491230 hasRelatedWork W2065737662 @default.
- W1525491230 hasRelatedWork W2068675427 @default.
- W1525491230 hasRelatedWork W2085171956 @default.
- W1525491230 hasRelatedWork W2158323279 @default.
- W1525491230 hasRelatedWork W2159009088 @default.
- W1525491230 hasRelatedWork W2227115705 @default.
- W1525491230 hasRelatedWork W2370807230 @default.
- W1525491230 hasRelatedWork W2405855851 @default.
- W1525491230 isParatext "false" @default.
- W1525491230 isRetracted "false" @default.
- W1525491230 magId "1525491230" @default.
- W1525491230 workType "dissertation" @default.