On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices |
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Authors: | Jinsong Chen Yijia Tan |
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Institution: | (1) College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian, 350002, P.R. China |
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Abstract: | Let n be a positive integer, and C
n
(r) the set of all n × n r-circulant matrices over the Boolean algebra B = {0, 1},
. For any fixed r-circulant matrix C (C ≠ 0) in G
n
, we define an operation “*” in G
n
as follows: A * B = ACB for any A, B in G
n
, where ACB is the usual product of Boolean matrices. Then (G
n
, *) is a semigroup. We denote this semigroup by G
n
(C) and call it the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix C. Let F be an idempotent element in G
n
(C) and M(F) the maximal subgroup in G
n
(C) containing the idempotent element F. In this paper, the elements in M(F) are characterized and an algorithm to determine all the elements in M(F) is given. |
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Keywords: | generalized ciculant Boolean matrix sandwich semigroup idempotent element maximal subgroup |
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