With your host… Alan Quebec

Group theory Orbits and counting Coding theoryPotpourri $100 $200 $300 $400 $500

The four group axioms

Bac k Closure Associativity Identity Inverses

A group with 11 elements is this kind of group

Bac k Cyclic

The easiest way to tell if a subset of G is a subgroup

Bac k Check that if x, y are elements of H, then so is xy -1

Why S 5 cannot have a subgroup of order 7

Bac k Lagrange’s Theorem

There are this many elements of order 13 in C 13

Bac k 12 (1 has order 1)

The difference between Gx and G x (Not just the names of the terms, but their meanings)

Bac k Gx is the orbit containing x; G x is the stabilizer of x

The size of an orbit if G = S 4

Bac k 4

The number of ways to color the edges of a pentagon red, green, and blue

Bac k

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

Bac k

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

Bac k Bac k Coefficient of rb 2 g 2 is

The number of errors that this code can correct for: 00000, 01100, 00111, 11001

Bac k 0 (minimum distance is 2)

The length of a codeword in the linear code given by the associated matrix

Bac k 7

The maximum number of codewords in a code of length 7 that can correct for one error

Bac k 16, since

The number of codewords in the linear code given by the associated matrix

Bac k 2 4 = 16

This is the smallest linear code that contains the codewords 001, 110

Bac k 000, 100, 011, 111 (code must be a group)

These three sets are all rings

Bac k

A ring that is not a field has this distinguishing characteristic

Bac k 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

Bac k Any matching power series that has a invertible constant term

The parity (even or odd) of the permutation (12345)

Bac k Even; decomposition into transpositions is (12)(23)(34)(45)

The order of the permutation (12)(345)

Bac k lcm(2, 3) = 6