In order to work through all possible combinations of a Rubik's Cube, the team then split all of the possibilities into 2.2 billion groups, known as cosets, each containing 20 billion positions. told the BBC that it would have been "completely hopeless" to try to compute all of the groups. ❋ Unknown (2010)
Rubik's Cube, the researchers split all of the possibilities into 2.2 billion groups, known as cosets, each containing 20 billion positions. ❋ Unknown (2010)
We let the elements of G/H be the (right) "cosets" Hg, for g in G. ❋ Unknown (2009)
So all the set of models we mentioned, orbifolds, cosets etc. are consistent backgrounds of classical string theory with no tachyons. ❋ Mark (2005)
They fit well in cosets, some under beds, others hanging from the ceiling, but no matter where you keep it, they make any tall job easier without standing on that stack of books, on top of a chair, on top of a step stool ... not that we've ever done that. ❋ Unknown (2010)
Each of these subproblems was small enough to fit in the memory of a modern PC, and the way we broke it down (mathematically, using cosets of the group generated by {U, F2, R2, D, B2, L2}, or more concisely, cosets of H) allowed us to solve each set rapidly. ❋ Unknown (2010)
Finally, we were able to distribute the 55,882,296 cosets of H among a large number of computers at Google and complete the computation in just a few weeks. ❋ Unknown (2010)
Just to explain a little: In quotientGp gs ks, we form the cosets of ks, and then we look at the action of the gs on the cosets by right multiplication - g sends Kh to Khg. So the elements of the quotient group are permutations of the cosets. ❋ Unknown (2009)
Here we have taken a subgroup H in D10, and then found the cosets Hx, Hy, for a couple of elements x, y in D10. ❋ Unknown (2009)
Thinking about this also subtly primes you for thinking about cosets and their relation to group actions (not so accessible to middle schoolers, but the priming is still there). ❋ Unknown (2009)
In the case above, we see that the quotient group can be generated by a single element, which simply swaps the two cosets. ❋ Unknown (2009)
The right cosets H x are defined similarly: partition the group G, any two cosets disjoint. ❋ Unknown (2008)
In general the two partitions of the group defined by the left cosets and by the right cosets are not the same. ❋ Unknown (2008)
A subgroup is [[normal subgroup | normal]] if and only if the left cosets agree with the right cosets for all elements. ❋ Unknown (2008)
The left cosets [[partition]] the group '' G '', any two cosets ❋ Unknown (2008)
This may be proved directly, or deduced from the observation that the left cosets are the ❋ Unknown (2008)
A subgroup is normal if the left cosets agree with the right cosets for all elements. ❋ Unknown (2008)
I [coset] you ❋ Trinny Buds (2023)
