Feb9-11, 04:43 PM
I am reading an article on the Reidemeister-Schreier
method for finding a presentation of a subgroup H of
a group G, given a presentation for G , in which this
statement is made:
A Schreier transversal of a subgroup H of F, free with
basis X, is a subset T of F such that for distinct
t in T, the cosets Ht are distinct, and the union of
the Ht is F, and such that ...
** every initial segment of an element of T itself
belongs to T **
Now, I understand that the cosets of H in G
partition G, and we select a subset T of G so that
Ht=/Ht' for t,t' in T, and \/Ht =G , but I have no
idea of what an initial segment would mean in this
context; are we assuming there is some sort of ordering
in T; maybe inherited from G ,or are we using
Well-Ordering Principle some how?
I thought we may have been considering the case where H
has infinite index in G, so that we assign a well-ordering in G
so that we can use Choice to select the least element g
representing the class Hg (i.e., all g_i in G with Hg_i=Hg ), but
I am not too clear on this.
Thanks for Any Ideas.
|Register to reply|
|Use Newton’s method with the specified initial approximation x1 to find x3.||Calculus & Beyond Homework||3|
|Ball rolling down a segment then up a parabolic segment||Introductory Physics Homework||4|
|KINETICS Initial RATES METHOD!||Biology, Chemistry & Other Homework||0|
|Initial Rates Method||Biology, Chemistry & Other Homework||1|
|Fitting points from a straight line segment onto a circular segment||Programming & Computer Science||3|