Problems in group theory
<p>Using combinatorial and character-theoretic methods the following theorems are proved.</p> <p><em>Theorem I</em> Let G be a finite simple group containing two non-conjugate subgroups A, B such that:</p> <p><ol type="i"&...
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| Format: | Thesis |
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1967
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| _version_ | 1826276814120550400 |
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| author | Stewart, W |
| author_facet | Stewart, W |
| author_sort | Stewart, W |
| collection | OXFORD |
| description | <p>Using combinatorial and character-theoretic methods the following theorems are proved.</p> <p><em>Theorem I</em> Let G be a finite simple group containing two non-conjugate subgroups A, B such that:</p> <p><ol type="i"><li><p>if a ε A, a &notequals; 1, then C<sub>G</sub> (a) = A; if b ε B, b &notequals; 1, then</p> <p>C<sub>G</sub>(b) = B;</p></li> <li>| N<sub>G</sub>(A)/A | = 2, | N<sub>G</sub>(B)/B | = 2.</li></ol></p> <p>Then G is isomorphic to some PSL (2,2<sup>a</sup>).</p> <p><em>Theorem II</em> Let G be a finite simple group containing a subgroup A such that:</p> <p><ol type="i"><li>if a ε A, a &notequals; 1, then C<sub>G</sub>(a) = A;</li> <li>| N<sub>G</sub>(A)/A | = 2;</li> <li>3 divides | A | .</li></ol></p> <p>Then G is isomorphic to some PSL (2,q).</p> |
| first_indexed | 2024-03-06T23:19:29Z |
| format | Thesis |
| id | oxford-uuid:6841b5f6-8bc0-407c-bad1-051381b56403 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:19:29Z |
| publishDate | 1967 |
| record_format | dspace |
| spelling | oxford-uuid:6841b5f6-8bc0-407c-bad1-051381b564032022-03-26T18:43:39ZProblems in group theoryThesishttp://purl.org/coar/resource_type/c_db06uuid:6841b5f6-8bc0-407c-bad1-051381b56403Polonsky Theses Digitisation Project1967Stewart, W<p>Using combinatorial and character-theoretic methods the following theorems are proved.</p> <p><em>Theorem I</em> Let G be a finite simple group containing two non-conjugate subgroups A, B such that:</p> <p><ol type="i"><li><p>if a ε A, a &notequals; 1, then C<sub>G</sub> (a) = A; if b ε B, b &notequals; 1, then</p> <p>C<sub>G</sub>(b) = B;</p></li> <li>| N<sub>G</sub>(A)/A | = 2, | N<sub>G</sub>(B)/B | = 2.</li></ol></p> <p>Then G is isomorphic to some PSL (2,2<sup>a</sup>).</p> <p><em>Theorem II</em> Let G be a finite simple group containing a subgroup A such that:</p> <p><ol type="i"><li>if a ε A, a &notequals; 1, then C<sub>G</sub>(a) = A;</li> <li>| N<sub>G</sub>(A)/A | = 2;</li> <li>3 divides | A | .</li></ol></p> <p>Then G is isomorphic to some PSL (2,q).</p> |
| spellingShingle | Stewart, W Problems in group theory |
| title | Problems in group theory |
| title_full | Problems in group theory |
| title_fullStr | Problems in group theory |
| title_full_unstemmed | Problems in group theory |
| title_short | Problems in group theory |
| title_sort | problems in group theory |
| work_keys_str_mv | AT stewartw problemsingrouptheory |