Product-Free Subsets of Groups, Then and Now
Dedicated to Joe Gallian on his 65th birthday and the 30th anniversary of the Duluth REU
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Mathematical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/64627 |
| _version_ | 1826211605482831872 |
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| author | Kedlaya, Kiran S. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kedlaya, Kiran S. |
| author_sort | Kedlaya, Kiran S. |
| collection | MIT |
| description | Dedicated to Joe Gallian on his 65th birthday and the 30th anniversary of the Duluth REU |
| first_indexed | 2024-09-23T15:08:38Z |
| format | Article |
| id | mit-1721.1/64627 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:08:38Z |
| publishDate | 2011 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/646272022-09-29T12:58:08Z Product-Free Subsets of Groups, Then and Now Kedlaya, Kiran S. Massachusetts Institute of Technology. Department of Mathematics Kedlaya, Kiran S. Kedlaya, Kiran S. Dedicated to Joe Gallian on his 65th birthday and the 30th anniversary of the Duluth REU Let G be a group. A subset S of G is product-free if there do not exist a, b, c ∈ S (not necessarily distinct1) such that ab = c. One can ask about the existence of large product-free subsets for various groups, such as the groups of integers (see next section), or compact topological groups (as suggested in [11]). For the rest of this paper, however, I will require G to be a finite group of order n > 1. Let α(G) denote the size of the largest product-free subset of G; put β(G) = α(G)/n, so that β(G) is the density of the largest product-free subset. What can one say about α(G) or β(G) as a function of G, or as a function of n? (Some of our answers will include an unspecified positive constant; I will always call this constant c.) 2011-06-21T15:27:21Z 2011-06-21T15:27:21Z 2009-01 Article http://purl.org/eprint/type/ConferencePaper 0-8218-4345-1 978-0-8218-4345-1 http://hdl.handle.net/1721.1/64627 Kedlaya, Kiran S. "Product-free subsets of groups, then and now." in Contemporary Mathematics, American Mathematical Society, v.479, p.169, 2009. en_US http://www.jointmathematicsmeetings.org/bookstore?fn=20&arg1=conmseries&ikey=CONM-479 Contemporary Mathematics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Mathematical Society Prof. Kedlaya via Michael Noga |
| spellingShingle | Kedlaya, Kiran S. Product-Free Subsets of Groups, Then and Now |
| title | Product-Free Subsets of Groups, Then and Now |
| title_full | Product-Free Subsets of Groups, Then and Now |
| title_fullStr | Product-Free Subsets of Groups, Then and Now |
| title_full_unstemmed | Product-Free Subsets of Groups, Then and Now |
| title_short | Product-Free Subsets of Groups, Then and Now |
| title_sort | product free subsets of groups then and now |
| url | http://hdl.handle.net/1721.1/64627 |
| work_keys_str_mv | AT kedlayakirans productfreesubsetsofgroupsthenandnow |