Isomorphism testing of groups of cube-free order

The modular isomorphism problem for the groups of order 512

For a prime p let G be a finite p-group and K a field of characteristic p. The Modular Isomorphism Problem (MIP) asks whether the modular group algebra KG determines the isomorphism type of G. We briefly survey the history of this problem and report on our computer-aided verification of the Modular Isomorphism Problem for the groups of order 512 and the field K with 2 elements.

Factoring elementary groups of prime cube order into subsets

Let p be a prime and let G be the 3-fold direct product of the cyclic group of order p. Rédei conjectured if G is the direct product of subsets A and B, each of which contains the identity element of G, then either A or B does not generate all of G. The paper verifies Rédei’s conjecture for p ≤ 11.

Isomorphism Classes and Derived Series of Certain Almost-Free Groups

Free Differential Calculus. II: The Isomorphism Problem of Groups

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THE ORDER GRAPHS OF GROUPS

Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we s...