Search results
Create the page "Transfinite induction" on this wiki! See also the search results found.
- ...his condition is called the ''nilpotency class'' of <math>G</math>. Using transfinite recursion, the notion of nilpotency class can be extended to any ordinal. To show that (2) implies (1), we note that it follows from induction that <math>C^k \subseteq G^k</math>; hence <math>C^{n+1}(G) = \{e\}</math>.9 KB (1,768 words) - 16:55, 5 June 2008
- ...= \{ e\}</math> is called the ''solvability class'' of <math>G</math>. By transfinite recursion, this notion can be extended to infinite ordinals, as well. ...en from the relation <math>(C^m(G),C^n(G)) \subseteq C^{m+n}(G)</math> and induction, we have2 KB (393 words) - 00:13, 2 June 2008
- It follows from [[transfinite induction]] that for each <math>j_0 \in J</math>,6 KB (1,183 words) - 14:02, 18 August 2009