REAL

Groups equal to a product of three conjugate subgroups

Cannon, John and Garonzi, Martino and Levy, Dan and Maróti, Attila and Simion, Iulian (2016) Groups equal to a product of three conjugate subgroups. ISRAEL JOURNAL OF MATHEMATICS, 215 (1). pp. 31-52. ISSN 0021-2172

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Abstract

Let G be a finite non-solvable group. We prove that there exists a proper subgroup A of G such that G is the product of three conjugates of A, thus replacing an earlier upper bound of 36 with the smallest possible value. The proof relies on an equivalent formulation in terms of double cosets, and uses the following theorem which is of independent interest and wider scope: Any group G with a BN-pair and a finite Weyl group W satisfies G=(Bn0B)2=BBn0B where n0 is any preimage of the longest element of W. The proof of the last theorem is formulated in the dioid consisting of all unions of double cosets of B in G. Other results on minimal length product covers of a group by conjugates of a proper subgroup are given.

Item Type: Article
Additional Information: Online first: 2014
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 04 Jan 2017 05:52
Last Modified: 04 Jan 2017 05:52
URI: http://real.mtak.hu/id/eprint/44209

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