scholarly journals Existence Proof Obligations for Constraints, Properties and Invariants in Atelier B

2020 ◽  
pp. 255-259
Author(s):  
Héctor Ruíz Barradas ◽  
Lilian Burdy ◽  
David Déharbe
Keyword(s):  
Existence Proof

The Existence ProofThe Existence Proof

PsycCRITIQUES ◽  
2015 ◽  
Vol 6060 (3030) ◽  
Author(s):  
Harry Whitaker ◽  
Emily DePetro
Keyword(s):  
Existence Proof

NATURAL EXISTENCE PROOF FOR LYONS SIMPLE GROUP

2003 ◽  
Vol 02 (03) ◽  
pp. 277-315
Author(s):  
GERHARD O. MICHLER ◽  
MICHAEL WELLER ◽  
KATSUSHI WAKI
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Conjugacy Classes ◽  
Existence Proof ◽  
Sporadic Simple Group ◽  
Character Tables ◽  
The Given ◽  
Fold Cover

In this article we give a self-contained existence proof for Lyons' sporadic simple group G by application of the first author's algorithm [18] to the given centralizer H ≅ 2A11 of a 2-central involution of G. It also yields four matrix generators of G inside GL 111 (5) which are given in Appendix A. From the subgroup U ≅ (3 × 2A8) : 2 of H ≅ 2A11, we construct a subgroup E of G which is isomorphic to the 3-fold cover 3McL: 2 of the automorphism group of the McLaughlin group McL. Furthermore, the character tables of E ≅ 3McL : 2 and G are determined and representatives of their conjugacy classes are given as short words in their generating matrices.

scholarly journals A geometric non-existence proof of an extremal additive code

2010 ◽  
Vol 117 (2) ◽  
pp. 128-137 ◽  
Author(s):  
Jürgen Bierbrauer ◽  
Stefano Marcugini ◽  
Fernanda Pambianco
Keyword(s):  
Existence Proof

Absolutely Free Algebras in a Topos Containing an Infinite Object

1976 ◽  
Vol 19 (3) ◽  
pp. 323-328 ◽  
Author(s):  
D. Schumacher
Keyword(s):  
Finite Sequence ◽  
Global Section ◽  
Free Algebras ◽  
Existence Proof

This note confirms that the existence proof for absolutely free algebras originated by Dedekind in [2] and completely developed for instance in [4] can still be carried out in a topos containing an infinite object i.e. an object N for which N ≃ N+1 if the type of the algebras considered is finite, pointed and internally projective i.e. is a finite sequence of objects, (Ij)i≤j≤k for which the functors ( )Ij preserve epimorphisms and each of which has a global section.

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