let l := u3(11). in this article, we classify groups with the same order and degree pattern as an almost simple group related to l. in fact, we prove that l, l:2 and l:3 are od-characterizable, and l:s3 is 5-fold od-characterizable.

A group homomorphism η : A → H is called a localization of A if every homomorphism φ : A→ H can be ‘extended uniquely’ to a homomorphism Φ : H → H in the sense that Φη = φ. This categorical concept, obviously not depending on the notion of groups, extends classical localizations as known for rings and modules. Moreover this setting has interesting applications in homotopy theory, see the introd...

The Algebraicity Conjecture treats model-theoretic foundations of algebraic group theory. It states that any simple group of finite Morley rank is an algebraic group over an algebraically closed field. In the mid-1990s a view was consolidated that this project falls into four cases of different flavour: even type, mixed type, odd type, and degenerate type. This book contains a proof of the conj...

0.1. For any finite group Γ, a “nonabelian Fourier transform matrix” was introduced in [L1]. This is a square matrix whose rows and columns are indexed by pairs formed by an element of Γ and an irreducible representation of the centralizer of that element (both defined up to conjugation). As shown in [L2], this matrix, which is unitary with square 1, enters (for suitable Γ) in the character for...

We prove that there exist k in and 0 < epsilon in such that every non-abelian finite simple group G, which is not a Suzuki group, has a set of k generators for which the Cayley graph Cay(G; S) is an epsilon-expander.