Isomorphism Classes of Uniform Groups

Computation of Isomorphism Classes of /»-Groups

p-groups may be classified by splitting the groups up into classes having the same commutator relations (isoclinism classes) and then determining the nonisomorphic groups in each class. This paper reduces the problem of determining the isomorphism classes to that of finding the equivalence classes of a set of matrices under some equivalence relation. A computer is used to find the equivalence c...

Isomorphism Classes of Maximal Intersecting Uniform Families Are Few

Denote by f(k,m) the number of isomorphism classes of maximal intersecting k-uniform families of subsets of [m]. In this note we prove the existence of a constant f(k) such that f(k,m) ≤ f(k) for all values of m.

Isomorphism Classes and Derived Series of Certain Almost-Free Groups

On isomorphism classes of generalized Fibonacci cubes

The generalized Fibonacci cube Qd(f) is the subgraph of the d-cube Qd induced on the set of all strings of length d that do not contain f as a substring. It is proved that if Qd(f) ∼= Qd(f ′) then |f | = |f ′|. The key tool to prove this result is a result of Guibas and Odlyzko about the autocorrelation polynomial associated to a binary string. An example of a family of such strings f , f ′, wh...

On the Isomorphism Classes of Transversals

In this paper, we prove that there does not exist a subgroup H of a finite group G such that the number of isomorphism classes of right transversals of H in G is two.