Timeline for What is the difference -- product/direct sum of cyclic groups
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 16, 2012 at 9:33 | vote | accept | frodo | ||
| Feb 16, 2012 at 0:02 | comment | added | Gerry Myerson | As to why you were given the question, maybe your instructor is using different definitions. Best to ask your instructor. | |
| Feb 16, 2012 at 0:00 | comment | added | Gerry Myerson | In the direct product of a countable infinity of groups, an element is an infinite sequence of elements of those groups. In the direct sum, same thing, only all but finitely many of the terms in the sequence must be the identity element. E.g., $(7,7,7,\dots)$ is in the direct product of infinitely many copies of the integers, but not in the direct sum. | |
| Feb 15, 2012 at 12:31 | comment | added | frodo | Thank you, Gerry. Hmm, then I really don't know why we are given this question. Anyways, 1) Out of curiosity, what happens when there are infinitely many? 2) Does it make any difference if say we consider the $C_n,C_m$ as rings of the form $Z_n,Z_m$? | |
| Feb 15, 2012 at 12:10 | history | answered | Gerry Myerson | CC BY-SA 3.0 |