التفاصيل البيبلوغرافية
| العنوان: |
Brauer's problem 21 for principal blocks. |
| المؤلفون: |
Moretó, Alexander1 (AUTHOR), Rizo, Noelia1 (AUTHOR), Fry, A. A. Schaeffer2 (AUTHOR) |
| المصدر: |
Transactions of the American Mathematical Society, Series B. 1/23/2025, Vol. 12, p38-64. 27p. |
| مصطلحات موضوعية: |
*CYCLIC groups, *ISOMORPHISM (Mathematics), *PROBLEM solving, *INTEGERS, *LOGICAL prediction |
| مستخلص: |
Problem 21 of Brauer's list of problems from 1963 asks whether for any positive integer k there are finitely many isomorphism classes of groups that occur as the defect group of a block with k irreducible characters. We solve this problem for principal blocks. Another long-standing open problem (from 1982) in this area asks whether the defect group of a block with 3 irreducible characters is necessarily the cyclic group of order 3. In most cases, we reduce this problem to a question on simple groups that is closely related to the recent solution of Brauer's height zero conjecture. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
Academic Search Index |