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Word maps with small image in simple groups
Word maps with small image simple groups Group Theory
2012/6/25
We construct non-power words which have small image in SL(2; 22n) for each n. In particular, the corresponding word maps are non-surjective. We also use this to construct word maps whose values are pr...
Abstract: Suppose $G$ is a simple group. For any nontrivial elements $g$ and $h$, $g$ can be written as a finite product of conjugates of $h$ or the inverse of $h$. G is called uniformly simple if the...
Abstract: The complete list of pairs of non-isomorphic finite simple groups having the same order is well-known. In particular for p>3, PSL_2(Z/p) is the "only" simple group of order (p^3-p)/2. It's l...
Product decompositions in finite simple groups
Product decompositions finite simple groups Group Theory
2011/8/30
Abstract: We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite s...
Torsion units in integral group rings of Conway simple groups
Zassenhaus conjecture torsion unit partial augmentation
2011/2/24
Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co1, Co2 and C...
We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups other than the alternating group of degree 5 admit unmixed Beauville structures. We also consider an analo...