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Groups and semigroups generated by a...

McCune, David.

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Groups and semigroups generated by automata.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Groups and semigroups generated by automata./
作者:	McCune, David.
面頁冊數:	100 p.
附註:	Source: Dissertation Abstracts International, Volume: 72-06, Section: B, page: .
Contained By:	Dissertation Abstracts International72-06B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3450101
ISBN:	9781124584096

Groups and semigroups generated by automata.
McCune, David.

Groups and semigroups generated by automata. - 100 p.

Source: Dissertation Abstracts International, Volume: 72-06, Section: B, page: .

Thesis (Ph.D.)--The University of Nebraska - Lincoln, 2011.

In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups "expanding automaton semigroups". We show that this class strictly contains the class of automaton semigroups, and we show that the class of asynchronous automaton semigroups strictly contains the class of expanding automaton semigroups. We demonstrate that undecidability arises in the actions of expanding automaton semigroups and semigroups arising from asynchronous automata on regular rooted trees. In particular, we show that one cannot decide whether or not an element of an asynchronous automaton semigroup has a fixed point. We show that expanding automaton semigroups are residually finite, while semigroups given by asynchronous automata need not be. We show that the class of expanding automaton semigroups is not closed under taking normal ideal extensions, but the class of semigroups given by asynchronous automata is closed under taking normal ideal extensions. We show that the class of expanding automaton semigroups is closed under taking direct products, provided that the direct product is finitely generated. We show that the class of automaton semigroups is not closed under passing to residually finite Rees quotients. We show that every partially commutative monoid is an automaton semigroup, and every partially commutative semigroup is an expanding automaton semigroup.

ISBN: 9781124584096Subjects--Topical Terms:

515831
Mathematics.

Groups and semigroups generated by automata.
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502 $a Thesis (Ph.D.)--The University of Nebraska - Lincoln, 2011.
520 $a In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups "expanding automaton semigroups". We show that this class strictly contains the class of automaton semigroups, and we show that the class of asynchronous automaton semigroups strictly contains the class of expanding automaton semigroups. We demonstrate that undecidability arises in the actions of expanding automaton semigroups and semigroups arising from asynchronous automata on regular rooted trees. In particular, we show that one cannot decide whether or not an element of an asynchronous automaton semigroup has a fixed point. We show that expanding automaton semigroups are residually finite, while semigroups given by asynchronous automata need not be. We show that the class of expanding automaton semigroups is not closed under taking normal ideal extensions, but the class of semigroups given by asynchronous automata is closed under taking normal ideal extensions. We show that the class of expanding automaton semigroups is closed under taking direct products, provided that the direct product is finitely generated. We show that the class of automaton semigroups is not closed under passing to residually finite Rees quotients. We show that every partially commutative monoid is an automaton semigroup, and every partially commutative semigroup is an expanding automaton semigroup.
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