The lattice of equational classes ofm-semigroups

Page, Warren; Butson, A. T.

doi:10.1007/bf02945109

Cited by 5 publications

(4 citation statements)

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“…noted here that if an m-group s a t i s f i e s any formal type of semi-abelianism, then i t i s at l e a s t (m-l)-semi-abelian. The above lemma, together with the following lemma due to Page and Butson[ 5 ] , will yield the proof of the main theorem.LEMMA 2 (Page and Butson). Let V be a non-commutative idempotent equational alass of L .…”

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confidence: 86%

“…Throughout the rest of the paper, the symbol p will stand for an arbitrary prime integer, and congruences will be written in the form x B y (mod t) . All other notation follows the conventions set forth in [5],…”

Section: Notation and P R E L I M I N A R I E Smentioning

confidence: 99%

“…In addition, it was shown [5] that the remaining atoms are actually m-groups in addition to being m-semigroups. The search for equationally complete classes of m-semlgroups has therefore been narrowed to special classes of non-abelian m-groups.…”

Section: Notation and P R E L I M I N A R I E Smentioning

confidence: 99%

“…Previous work by Page and Bu+son [5] and Post [6] is used to prove the conjecture (Page [4]) that every equationally complete m-group is at least weakly commutative; that i s , y-semi-abelian, where n-l|w-l . Use is then made of this new tool in the special case m = h , where two additional infinite families of equationally complete m-groups are determined.…”

Section: C O N C L U S I O Nmentioning

confidence: 99%

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Equationally complete varieties of generalized groups

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1975

Bull. Austral. Math. Soc.

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In previous work, Page and Butson [Algebra Universalis 3 (1973), 112-126] characterized all equationally complete classes (atoms) of m-semigroups (universal algebras with one m-ary associative operation), and hence /n-groups, in the commutative case. The further characterization of the non-commutative m-group atoms was thought to hinge upon a conjecture by Page [PhD thesis,-University of Miami, 1973] that a weaker form of commutativity held true. In this paper that conjecture is proved and then used to study the special case m = k . Two additional infinite sets of atoms are thereby determined, although i t is not proved that these examples exhaust the remaining atoms for m = h .

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confidence: 86%

Section: Notation and P R E L I M I N A R I E Smentioning

confidence: 99%

Section: Notation and P R E L I M I N A R I E Smentioning

confidence: 99%

Section: C O N C L U S I O Nmentioning

confidence: 99%

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