|"Using the axiom of choice, we prove that given any group G and subgroup H, there always exists a common system of coset representatives of the left and right cosets of H in G."|
Update of Sept. 11, 2005:
Dharwadker has changed his claim. He now says,
"Using the axiom of choice, we prove that given any group G and a finite subgroup H, there always exists a common system of coset representatives of the left and right cosets of H in G."
This new claim avoids the difficulty described by Schauenburg above, since H is now assumed to be finite. It also meets the following conditions stated by Fred Galvin (sci.math, Feb. 20, 2003):
"... if H is a finite subgroup of a (finite or infinite) group G, then there is a common transversal for the system of left cosets and the system of right cosets. This is still true for an infinite subgroup of finite index, but it breaks down for infinite subgroups of infinite index.
See L. Mirsky, Transversal Theory, Academic Press, 1971, ISBN 0-12-498550-5."
From Wikipedia on 31 May, 2007:
Shown below is a list of 25 alterations to Wikipedia math articles made today by user 188.8.131.52.
All of the alterations involve removal of links placed by user Cullinane (myself).
The 122.163... IP address is from an internet service provider in New Delhi, India.
The New Delhi anonymous user was apparently inspired by an earlier
blitz by Wikipedia administrator Charles Matthews....
Ashay Dharwadker and Usenet Postings
and Talk: Four color theorem/Archive 2.
See also some recent comments from 122.163...
at Talk: Four color theorem.
May 31, 2007, alterations by
The deletions should please Charles Matthews and fans of Ashay Dharwadker's work as a four-color theorem enthusiast and as editor of the Open Directory sections on combinatorics and on graph theory.
There seems little point in protesting the deletions while Wikipedia still allows any anonymous user to change their articles.
-- Cullinane 23:28, 31 May 2007
OF THE STANDARD MODEL WITH QUANTUM GRAVITY
by Ashay Dharwadker