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Involutory decomposition of groups into twisted subgroups and subgroups
 J. Group Theory
, 2000
"... Gyrogroups are generalized groups modelled on the Einstein groupoid of all relativistically admissible velocities with their Einstein’s velocity addition as a binary operation. Einstein’s gyrogroup fails to form a group since it is nonassociative. The breakdown of associativity in the Einstein addit ..."
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Gyrogroups are generalized groups modelled on the Einstein groupoid of all relativistically admissible velocities with their Einstein’s velocity addition as a binary operation. Einstein’s gyrogroup fails to form a group since it is nonassociative. The breakdown of associativity in the Einstein addition does not result in loss of mathematical regularity owing to the presence of the relativistic effect known as the Thomas precession which, by abstraction, becomes an automorphism called the Thomas gyration. The Thomas gyration turns out to be the missing link that gives rise to analogies shared by gyrogroups and groups. In particular, it gives rise to the gyroassociative and the gyrocommuttive laws that Einstein’s addition possesses, in full analogy with the associative and the commutative laws that vector addition possesses in a vector space. The existence of striking analogies shared by gyrogroups
Moufang loops with commuting inner mappings
 J. Pure Appl. Algebra
, 2009
"... Abstract. We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at most two. 6divisible Moufang loops with commuting inner mappings have nilpotency class at most two. There is ..."
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Abstract. We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at most two. 6divisible Moufang loops with commuting inner mappings have nilpotency class at most two. There is a Moufang loop of order 214 with commuting inner mappings and of nilpotency class three. 1.
BRUCK LOOPS WITH ABELIAN INNER MAPPING GROUPS
"... Bruck loops with abelian inner mapping groups are centrally nilpotent of class at most 2. ..."
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Bruck loops with abelian inner mapping groups are centrally nilpotent of class at most 2.
Loops with abelian inner mapping groups: An application of automated deduction
 Automated Reasoning and Mathematics  Essays in Memory of William W. McCune, volume 7788 of LNCS
, 2013
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Comment.Math.Univ.Carolin. 45,2 (2004)213–221 213
"... On loops whose inner permutations commute ..."
Comment.Math.Univ.Carolinae 41,2 (2000)415{427 415 Loops and quasigroups: Aspects of current work and
"... prospects for the future ..."