Equation 677 Database

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Magma eca9f8db0d2d…

magma eca9f8db0d2d
Size
707
Isomorphism class hash
eca9f8db0d2dd3885af068f152ac461abfaae860126da5d2bc0801f1e00b9ed0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 18:09:44
Display reorder
593,592,591,589,590,588,639,197,193,192,195,196,194,102,107,103,104,105,106,304,303,305,300,301,302,297,296,298,299,294,295,258,263,259,260,261,262,11,10,6,7,8,9,79,78,80,81,82,83,210,215,211,212,213,214,161,160,156,157,158,159,87,89,86,84,85,88,183,182,184,185,180,181,357,356,359,358,354,355,490,489,491,494,492,493,417,419,418,416,414,415,361,362,360,365,363,364,579,578,580,583,581,582,534,533,535,531,532,530,566,568,567,569,570,571,465,467,466,469,470,468,478,477,479,480,481,482,611,606,613,621,622,607,625,632,668,688,650,676,697,675,698,689,700,705,690,706,228,230,229,232,233,231,19,18,20,21,22,23,53,52,48,49,50,51,40,39,41,36,37,38,139,138,140,141,142,143,151,150,152,153,154,155,289,288,290,291,292,293,25,24,26,27,28,29,129,128,130,131,126,127,287,283,286,284,285,282,123,122,124,125,120,121,250,249,251,246,247,248,514,513,515,540,516,517,550,552,551,549,547,548,587,543,539,537,538,536,560,559,561,564,562,563,427,426,428,430,431,429,442,444,443,445,446,565,572,574,573,576,577,575,461,460,459,463,464,462,609,618,608,610,635,619,617,620,669,671,672,655,703,663,679,657,685,691,662,701,92,94,93,90,91,95,338,337,339,340,341,336,317,316,312,313,314,315,239,238,234,235,236,237,253,252,254,255,256,257,311,310,306,307,308,309,31,30,32,33,34,35,225,224,226,227,222,223,100,99,101,96,97,98,144,146,149,147,148,145,15,14,16,17,12,13,113,112,108,109,110,111,502,501,503,506,504,505,520,519,518,522,523,521,472,471,473,474,475,476,512,511,510,507,508,509,594,595,596,598,599,597,379,378,380,382,383,381,368,367,366,369,370,371,387,389,388,386,384,385,634,628,627,624,633,629,630,631,664,694,681,677,695,666,683,670,696,693,652,704,350,352,351,348,349,353,323,322,318,319,320,321,244,243,245,240,241,242,77,76,72,73,74,75,68,67,69,70,71,66,64,63,65,60,61,62,275,274,270,271,272,273,45,44,46,47,42,43,269,268,264,265,266,267,281,277,280,278,279,276,54,59,55,56,57,58,2,0,3,4,5,1,602,601,600,603,604,605,558,557,556,554,555,553,450,452,451,449,447,448,391,390,392,395,393,394,454,453,455,457,458,456,439,438,440,541,542,441,544,546,545,586,584,585,436,435,437,432,433,434,616,636,626,644,643,623,614,615,656,699,648,686,692,667,678,680,682,684,665,702,206,208,207,204,205,209,166,165,167,162,163,164,132,137,133,134,135,136,187,186,188,189,190,191,178,177,179,174,175,176,168,173,169,170,171,172,117,116,118,119,114,115,203,202,198,199,200,201,330,335,331,332,333,334,342,344,347,345,346,343,328,327,329,324,325,326,217,216,218,219,220,221,485,484,483,486,487,488,499,498,500,495,496,497,375,377,376,374,372,373,526,525,524,527,528,529,410,409,408,413,411,412,420,422,421,423,424,425,406,405,407,404,402,403,401,400,399,397,398,396,641,637,642,638,640,612,646,645,659,674,649,660,687,651,654,653,658,661,647,673 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#10d95f4d62da29d597cabb26c5d7a2889acb76e08f2897cdd164594c6bfbc5c4, M = {90, 91, 92, 93, 94, 95, 134} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-07 18:09:45 · history