Equation 677 Database

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Magma df19a3b7ebd6…

magma df19a3b7ebd6
Size
707
Isomorphism class hash
df19a3b7ebd6939d40aa98177ad95e9c959be6478196b546e1d3eeecdadb5e03
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
2026-10-06 19:49:44
Display reorder
244,243,245,240,241,242,706,293,292,288,289,290,291,45,42,46,47,44,43,99,98,100,101,96,97,2,0,3,4,5,1,282,287,283,284,285,286,260,259,261,262,263,258,187,186,188,189,190,191,204,209,205,206,207,208,305,304,301,300,302,303,298,299,294,296,297,295,431,433,432,429,430,428,526,525,524,528,529,527,547,546,548,549,550,551,446,448,447,451,449,450,484,483,482,485,486,487,497,499,498,495,496,494,481,480,479,477,478,476,399,533,400,403,401,402,409,408,407,405,406,404,562,561,563,558,560,559,609,617,611,607,618,608,642,625,640,638,699,674,694,703,698,679,700,704,705,702,132,137,133,134,135,136,85,88,86,87,84,89,155,154,150,151,152,153,142,141,143,138,139,140,53,52,48,49,50,51,66,71,67,68,69,70,12,17,13,14,15,16,251,250,246,247,248,249,266,264,267,268,269,265,122,121,123,124,125,120,536,535,534,537,538,539,503,505,504,502,500,501,462,461,463,458,459,460,381,383,382,386,384,385,470,472,471,474,475,473,360,362,361,358,359,357,464,466,465,469,467,468,308,306,307,309,310,311,575,574,573,570,572,571,555,556,552,553,554,557,633,634,631,632,630,606,635,615,629,637,701,691,695,683,669,666,675,676,684,685,270,271,272,273,274,275,179,176,174,175,178,177,185,184,180,181,182,183,198,203,199,200,201,202,172,171,173,168,169,170,213,212,214,215,210,211,146,145,147,148,149,144,65,64,60,61,62,63,93,92,94,95,90,91,58,57,59,54,55,56,426,425,427,424,422,423,416,418,417,421,419,420,511,510,509,507,508,506,413,415,414,412,410,411,368,367,366,363,364,365,317,316,315,312,313,314,395,394,393,397,398,396,346,345,347,350,348,349,564,565,566,567,568,569,545,544,543,542,540,541,613,627,626,614,612,628,639,616,641,636,692,693,680,686,664,671,670,687,678,696,277,281,276,278,279,280,219,216,220,221,218,217,117,116,118,119,114,115,111,110,112,113,108,109,9,8,10,11,7,6,236,235,237,238,239,234,72,77,73,74,75,76,223,222,224,225,226,227,257,256,252,253,254,255,78,83,79,80,81,82,376,375,377,380,378,379,602,600,601,604,605,603,514,513,512,516,517,515,371,370,369,373,374,372,580,579,581,578,577,576,338,337,336,339,340,341,584,582,583,586,587,585,596,594,595,597,598,599,389,388,387,391,392,390,589,590,588,591,592,593,647,644,648,645,646,643,651,653,650,654,697,677,681,690,672,667,673,689,682,688,159,158,160,161,156,157,29,26,24,25,28,27,32,31,33,34,35,30,231,230,232,233,228,229,22,21,23,18,19,20,131,130,126,127,128,129,106,105,107,102,103,104,164,163,165,166,167,162,38,37,39,40,41,36,193,192,194,195,196,197,355,354,356,353,351,352,492,491,493,488,489,490,323,322,321,319,320,318,531,530,532,343,344,342,456,455,457,454,452,453,445,444,443,440,441,442,333,335,334,332,330,331,328,327,329,326,324,325,439,438,437,435,436,434,520,519,518,523,521,522,621,649,610,619,620,622,652,623,624,655,663,659,661,665,657,656,658,662,660,668 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#96b028d3c6de0cbaff964417289f690895c6af42769867ad5a7d2affbed8a752, M = {12, 13, 14, 15, 16, 17, 143} 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 2026-10-06 19:49:45 · history