Equation 677 Database

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Magma aa707ae89d15…

magma aa707ae89d15
Size
396
Isomorphism class hash
aa707ae89d155754203c2c02899790084923fac39692bfc602d51c7582a3cda1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-05 11:07:19
Display reorder
376,354,311,332,307,25,312,266,4,265,16,270,5,271,17,276,6,277,18,163,7,171,19,333,308,316,313,334,8,28,20,164,9,21,29,165,10,22,30,166,11,23,31,167,12,24,32,168,13,314,315,335,309,310,26,169,14,15,27,170,3,161,153,154,155,156,157,158,159,160,329,162,330,331,328,362,387,381,382,389,351,204,240,272,269,193,241,278,275,194,230,185,120,195,231,186,121,196,232,187,122,197,233,363,358,340,234,188,123,198,235,189,199,124,345,338,341,359,346,339,342,2,236,190,200,0,237,191,201,306,366,364,202,1,238,192,203,263,239,267,94,86,87,88,89,90,91,92,93,95,82,83,84,85,325,375,384,379,393,373,361,360,77,281,152,137,78,282,139,138,79,283,140,125,80,280,141,126,81,287,142,127,67,288,143,128,68,290,144,129,69,145,292,130,70,146,294,131,71,147,296,132,72,148,298,133,73,149,300,134,74,150,302,135,75,151,304,136,76,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,385,394,395,383,356,353,321,109,43,273,48,110,33,279,49,96,34,254,50,97,317,349,357,98,35,255,51,99,36,256,52,100,37,257,53,101,258,38,54,102,350,355,319,103,259,39,44,104,260,40,45,105,261,41,46,106,262,42,47,107,368,318,320,108,253,245,246,247,248,249,250,251,252,242,243,244,347,348,367,378,386,390,392,372,352,322,174,218,268,56,175,219,274,57,176,220,111,58,177,221,112,59,178,222,113,60,179,223,114,61,180,224,115,62,181,116,225,323,336,326,365,324,337,327,226,63,182,117,227,64,183,118,228,65,184,119,229,66,172,264,217,55,173,205,210,211,212,213,214,215,216,206,207,208,209,343,344,371,391,377,388,380 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#82fda0c11d8b67dd90198c9d834359ac6146390672939dae5a097a0c09da5164, M = {75} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 79): MacNeish's product over GF(79); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-05 11:07:20 · history