Loubere IMagic Squares Semigroups and Groups
Keywords:
semigroup, group, centre piece, eigen values, subelement, magic sum
Abstract
This work is a pioneer investigation of semigroups and groups over the Loube re Magic Squares By the Loube re Magic Squares we understand the magic squares formed by the De La Loube re Procedure The set of the Loube re Magic Squares equipped with the matrix binary operation of addition forms a semigroup if the underlining set so considered is the multi set of natural numbers and if we consider the multi set of integer numbers as the underlined set of entries of the square the set of the squares enclosed with the aforementioned operation forms an abelian group The Loube re Magic Squares are always recognized with centre piece C and magic sum M S We showcase that the set of the centre pieces and the set of the magic sums form respective abelian groups if both are equipped with integer numbers operation of addition We also explicate that the set of the eigen values of the squares enclosed with the integer addition operation forms an abelian group We reveal that the subelement a terminology we introduced Magic Squares of the Loube re Magic Squares forms a semigroup and the Subelement Magic Squares of the Loube re Magic Squares Group forms a group with respect to the matrix binary operation of addition
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Published
2015-01-15
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