Embed Size (px)
DESCRIPTION
With your host… Alan Quebec. The four group axioms. Closure Associativity Identity Inverses. Back. A group with 11 elements is this kind of group. Cyclic. Back. The easiest way to tell if a subset of G is a subgroup. Check that if x, y are elements of H, then so is xy -1. Back. - PowerPoint PPT Presentation
Citation preview
With your host…Alan Quebec
Group theory Orbits and counting
Coding theory Potpourri
$100 $100 $100 $100$200 $200 $200 $200$300 $300 $300 $300$400 $400 $400 $400
$500 $500 $500 $500
The four group axioms
Back
ClosureAssociativity
IdentityInverses
A group with 11 elements is this kind of group
Back
Cyclic
The easiest way to tell if a subset of G is a subgroup
Back
Check that if x, y are elements of H, then so is
xy-1
Why S5 cannot have a subgroup of order 7
Back
Lagrange’s Theorem
There are this many elements of order 13 in
C13
Back
12 (1 has order 1)
The difference between Gx and Gx(Not just the names of the terms, but their meanings)
Back
Gx is the orbit containing x; Gx is the stabilizer of x
The size of an orbit if G = S4
Back
4
The number of ways to color the edges of a pentagon red, green,
and blue
Back
The number of ways to place colored pie slices into a Trivial Pursuit game piece like
the one below, if only the orange and yellow pieces can be used
Back
The number of ways to color the edges of a pentagon red, green, and blue where 2 edges are green and 2
edges are blue
Back
Back
Coefficient of rb2g2 is
The number of errors that this code can correct for:00000, 01100, 00111, 11001
Back
0 (minimum distance is 2)
The length of a codeword in the linear code given by the
associated matrix
Back
7
The maximum number of codewords in a code of length 7 that can correct for one
error
Back
16, since
The number of codewords in the linear code given by the
associated matrix
Back
24 = 16
This is the smallest linear code that contains the codewords
001, 110
Back
000, 100, 011, 111(code must be a group)
These three sets are all rings
Back
A ring that is not a field has this distinguishing
characteristic
Back
Not all nonzero elements have multiplicative inverses
This is an example of an invertible power series where all coefficients are nonzero and the coefficient of
is 10
Back
Any matching power series that has a invertible constant term
The parity (even or odd) of the permutation (12345)
Back
Even; decomposition into transpositions is (12)(23)(34)(45)
The order of the permutation(12)(345)
Back
lcm(2, 3) = 6
