Revision as of 19:33, 18 December 2009 edit RDBury (talk \| contribs) Autopatrolled, Extended confirmed users, Pending changes reviewers 11,806 edits Removed essay tag, did not seem appropriate in this case. ← Previous edit		Revision as of 19:51, 18 December 2009 edit undo Michael Hardy (talk \| contribs) Administrators 210,577 edits →Properties: \ell Next edit →
Line 21: ==Properties== A group with a length function does ''not'' form a [[filtered group]], meaning that the [[sublevel set]]s <math>S_i := \{g \mid l\ell(g) \leq i\}</math> do not form subgroups in general. However, the [[group ring\|group algebra]] of a group with a length functions forms a [[filtered algebra]]: the axiom <math>l\ell(gh) \leq l\ell(g)+l\ell(h)</math> corresponds to the filtration axiom. ----

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