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Arithmetic conditions relating particle masses can be defined on the basis of (1) the supersymmetric conservation of congruence and (2) the observed characteristics of particle reactions and stabilities. Stated in the form of common divisors, these relations can be interpreted as expressions of genetic elements that represent specific particle characteristics. In order to illustrate this concept, it is shown that the pion triplet ({pi}{sup {+-}}, {pi}{sup 0}) can be associated with the existence of a greatest common divisor d{sub 0{+-}} in a way that can account for both the highly similar physical properties of these particles and the observed {pi}{sup {+-}}/{pi}{sup 0} mass splitting. These results support the conclusion that a corresponding statement holds generally for all particle multiplets. Classification of the respective physical states is achieved by assignment of the common divisors to residue classes in a finite field F{sub P{sub {alpha}}} and the existence of the multiplicative group of units F{sub P{sub {alpha}}} enables the corresponding mass parameters to be associated with a rich subgroup structure. The existence of inverse states in F{sub P{sub {alpha}}} allows relationships connecting particle mass values to be conveniently expressed in a form in which the genetic divisor structure is prominent. An example is given in which the masses of two neutral mesons (K{degree} {r_arrow} {pi}{degree}) are related to the properties of the electron (e), a charged lepton. Physically, since this relationship reflects the cascade decay K{degree} {r_arrow} {pi}{degree} + {pi}{degree}/{pi}{degree} {r_arrow} e{sup +} + e{sup {minus}}, in which a neutral kaon is converted into four charged leptons, it enables the genetic divisor concept, through the intrinsic algebraic structure of the field, to provide a theoretical basis for the conservation of both electric charge and lepton number. It is further shown that the fundamental source of supersymmetry can be expressed in terms of hierarchical relationships between odd and even order subgroups of F{sub P{sub {alpha}}}, an outcome that automatically reflects itself in the phenomenon of fermion/boson pairing of individual particle systems. Accordingly, supersymmetry is best represented as a group rather than a particle property. The status of the Higgs subgroup of order 4 is singular; it is isolated from the hierarchical pattern and communicates globally to the mass scale through the seesaw congruence by (1) fusing the concepts of mass and space and (2) specifying the generators of the physical masses

Determination of Supersymmetric Particle Masses and Attributes with Genetic Divisors