Timeline for Generalized free product of semigroups with amalgamated subsemigroups
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 1, 2013 at 1:51 | history | undeleted | user6976 | ||
| Jul 28, 2013 at 22:29 | history | deleted | user6976 | via Vote | |
| Jul 28, 2013 at 20:52 | comment | added | Boris Novikov | @ Mark Sapir: No, Mark. My question is "who consider". If nobody, we have to give definitions, establish simple properties etc. We have not "academic" interest, this construction appeared in our problems. Secondly, "it is just a composition of amalgamated products with one amalgamated subgroup each" - again, no. In the cited paper of Hanna Neumann several amalgamated subgroups were considered. | |
| Jul 28, 2013 at 19:56 | comment | added | user6976 | @Boris: The question was "where was it used". The answer is "nowhere" because the construction is too general. Neumann's construction is much more useful. But it is just a composition of amalgamated products with one amalgamated subgroup each. | |
| Jul 28, 2013 at 16:59 | comment | added | Boris Novikov | I have a special case, so maybe... | |
| Jul 28, 2013 at 16:48 | comment | added | user6976 | The problem whether $G_i$ embed into the product is undecidable. In fact the word problem is not necessarily decidable for amalgamated product of two finite semigroups with one amalgamated subsemigroup, even if you assume that both semigroups embed. It was proved by Kublanovsky and myself. | |
| Jul 28, 2013 at 16:37 | comment | added | Boris Novikov | Thank you very much. But in general the semigroups $G_i$ don't embed into this construction, and first of all I am interested just by this topic. Of course, I understand that this topic is too complicated, so I didn't include it into my question. | |
| Jul 28, 2013 at 15:14 | history | answered | user6976 | CC BY-SA 3.0 |