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Abstract: We introduce the notion of quasi‐orthogonal cocycle. This is motivated in part by the maximal determinant problem for square { ± 1 }‐matrices of size congruent to 2 modulo 4. Quasi‐orthogonal cocycles are analogous to the orthogonal cocycles of algebraic design theory. Equivalences with new and known combinatorial objects afforded by this analogy, such as quasi‐Hadamard groups, relative quasi‐difference sets, and certain partially balanced incomplete block designs, are proved. [ABSTRACT FROM AUTHOR]

We survey the legacy of L. G. Kovács in linear group theory, with a particular focus on classification questions. [ABSTRACT FROM PUBLISHER]

For n = 2,3 and finite field 피 of characteristic greater than n, we provide a complete and irredundant list of soluble irreducible subgroups of GL(n,피). The insoluble irreducible subgroups of GL(2,피) are similarly determined. Each group is given explicitly by a generating set of matrices. The lists are available electronically. [ABSTRACT FROM AUTHOR]