Equation 677 Database

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Magma cc06a42f0a06…

magma cc06a42f0a06
Size
451
Isomorphism class hash
cc06a42f0a06775e16ab50bd0ea2443068c62b2b15295bff622f7633030f8c35
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 450) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 08:51:20
Display reorder
440,442,443,449,441,444,445,446,447,448,450,237,311,161,47,180,141,93,325,339,223,238,312,162,48,181,142,94,326,340,224,313,239,163,49,182,143,95,327,341,225,314,240,164,50,183,144,88,328,342,226,307,241,157,43,184,145,89,329,343,219,242,220,308,158,44,185,146,90,330,344,309,221,235,159,45,186,147,91,323,345,236,310,222,160,46,187,148,92,324,351,7,8,14,28,10,11,6,22,373,372,374,375,376,377,378,379,380,381,383,382,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,423,431,422,424,425,426,427,428,429,430,353,361,352,354,355,356,357,358,359,360,363,362,371,364,365,366,367,368,369,370,434,439,435,437,438,432,433,436,86,252,105,286,199,60,121,51,272,306,87,253,104,287,200,61,122,52,273,299,254,80,108,288,201,62,123,53,274,300,255,81,106,289,202,63,124,54,267,301,256,82,103,290,203,64,118,55,268,302,83,303,257,102,283,196,65,119,56,269,258,304,84,109,284,197,58,120,57,270,85,251,305,107,285,198,59,348,346,271,12,13,16,30,18,24,29,20,151,335,250,316,217,231,39,177,138,111,152,336,243,317,218,232,40,178,139,112,337,153,244,318,211,233,42,179,140,113,338,154,245,319,212,234,33,173,133,114,331,155,246,320,213,227,32,174,134,115,156,116,332,247,321,214,228,34,175,135,333,117,149,248,322,215,229,35,176,136,150,334,110,249,315,216,230,41,349,137,0,2,3,5,15,21,26,4,265,72,165,291,125,280,74,194,209,96,266,73,166,292,126,281,75,195,210,101,66,259,167,293,127,282,76,188,204,97,67,260,168,294,128,275,99,189,205,100,68,261,169,295,129,276,77,190,206,98,262,36,69,170,296,130,277,78,191,207,70,37,263,171,297,131,278,79,192,208,264,71,38,172,298,132,279,347,193,350,9,1,17,31,19,23,27,25 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 451 = 11 + 5*88, 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#19db9b9ff88013075cd50c08e95878a5b21c7b46c92f96bdfba1d02cb4f8d3d6, M = {88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98} 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, 88): MacNeish's product over GF(8) x GF(11); GF(8) = F_2[x]/(x^3 + x + 1); 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: 11.

last edited by qawbecrdtey at 2026-10-06 08:51:21 · history