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- W2562876490 abstract "Abstract For a given integer <m:math xmlns:m=http://www.w3.org/1998/Math/MathML display=inline> <m:mi>n</m:mi> <m:mo>=</m:mo> <m:msubsup> <m:mi>p</m:mi> <m:mn>1</m:mn> <m:mrow> <m:msub> <m:mi>α</m:mi> <m:mn>1</m:mn> </m:msub> </m:mrow> </m:msubsup> <m:msubsup> <m:mi>p</m:mi> <m:mn>2</m:mn> <m:mrow> <m:msub> <m:mi>α</m:mi> <m:mn>2</m:mn> </m:msub> </m:mrow> </m:msubsup> <m:mo>⋯</m:mo> <m:msubsup> <m:mi>p</m:mi> <m:mi>k</m:mi> <m:mrow> <m:msub> <m:mi>α</m:mi> <m:mi>k</m:mi> </m:msub> </m:mrow> </m:msubsup> </m:math> $n = p_1^{alpha _1 } p_2^{alpha _2 } cdots p_k^{alpha _k }$ ( k ≥ 2), we give here a class of finitely presented finite monoids of order n . Indeed the monoids Mon (π), where <m:math xmlns:m=http://www.w3.org/1998/Math/MathML display=block> <m:mo>π</m:mo> <m:mo>=</m:mo> <m:mrow> <m:mo stretchy=false>〈</m:mo> <m:mrow> <m:msub> <m:mi>a</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mi>a</m:mi> <m:mn>2</m:mn> </m:msub> <m:mo>,</m:mo> <m:mo>…</m:mo> <m:mo>,</m:mo> <m:msub> <m:mi>a</m:mi> <m:mi>k</m:mi> </m:msub> <m:mo stretchy=false>|</m:mo> <m:msubsup> <m:mi>a</m:mi> <m:mi>i</m:mi> <m:mrow> <m:msubsup> <m:mi>p</m:mi> <m:mi>i</m:mi> <m:mrow> <m:msub> <m:mi>α</m:mi> <m:mi>i</m:mi> </m:msub> </m:mrow> </m:msubsup> </m:mrow> </m:msubsup> <m:mo>=</m:mo> <m:mrow> <m:msub> <m:mi>a</m:mi> <m:mi>i</m:mi> </m:msub> <m:mo>,</m:mo> <m:mo> </m:mo> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>i</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mo>…</m:mo> <m:mo>,</m:mo> <m:mi>k</m:mi> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msub> <m:mi>a</m:mi> <m:mi>i</m:mi> </m:msub> <m:msub> <m:mi>a</m:mi> <m:mrow> <m:mi>i</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:msub> <m:mi>a</m:mi> <m:mi>i</m:mi> </m:msub> <m:mo>,</m:mo> <m:mo> </m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>i</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mo>…</m:mo> <m:mo>,</m:mo> <m:mi>k</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=false>〉</m:mo> </m:mrow> <m:mo>.</m:mo> </m:math> $$pi = {langle {a_1 ,a_2 , ldots ,a_k |a_i^{p_i^{alpha _i } } = {a_i}, {left({i = 1,2, ldots ,k} right)}, a_i a_{i + 1} = {a_i}, left({i = 1,2, ldots ,k - 1} right)} rangle} .$$ As a result of this study we are able to classify a wide family of the k- generated p -monoids (finite monoids of order a power of a prime p ). An interesting di erence between the center of finite p -groups and the center of finite p -monoids has been achieved as well. All of these monoids are regular and non-commutative." @default.
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- W2562876490 date "2014-06-01" @default.
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- W2562876490 title "Non-commutative finite monoids of a given order <i>n</i> ≥ 4" @default.
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- W2562876490 doi "https://doi.org/10.2478/auom-2014-0028" @default.
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