Equation 677 Database

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Magma a636f538d53a…

magma a636f538d53a
Size
707
Isomorphism class hash
a636f538d53a3bd19e0af7d7d2581e8dd8d3e7c28ead6a87c4eaaf381b78b0ce
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 21:53:48
Display reorder
296,295,297,298,299,294,706,57,59,54,55,56,58,62,61,63,64,65,60,332,330,333,334,335,331,322,321,323,318,319,320,305,304,300,301,302,303,313,312,314,315,316,317,285,284,286,287,282,283,229,228,230,231,232,233,155,154,150,151,152,153,109,108,110,111,112,113,207,206,208,209,204,205,535,534,533,538,536,537,523,522,521,526,524,525,343,342,344,345,346,347,466,465,464,463,461,462,584,582,583,587,585,586,378,380,379,382,383,381,410,409,408,412,413,411,513,512,514,509,510,511,551,553,552,556,554,555,628,606,609,627,610,607,649,638,643,698,671,668,662,688,702,699,693,700,705,703,146,148,149,144,145,147,251,250,247,246,248,249,5,4,1,0,2,3,117,116,118,119,114,115,196,195,197,192,193,194,84,89,85,86,87,88,176,175,177,178,179,174,169,168,170,171,172,173,245,244,241,240,242,243,189,188,190,191,186,187,95,94,90,91,92,93,548,550,549,546,545,547,519,518,520,516,517,515,493,492,491,495,496,494,603,605,604,600,601,602,489,488,490,486,487,485,507,506,508,505,503,504,573,575,572,570,571,569,445,444,446,447,448,557,561,563,562,560,558,559,608,624,611,630,631,625,637,639,636,690,675,680,652,667,689,679,676,681,697,696,132,134,135,136,137,133,167,166,162,163,164,165,220,219,221,216,217,218,9,8,10,11,6,7,182,181,183,184,185,180,292,291,293,288,289,290,123,122,124,125,120,121,141,140,142,143,138,139,254,253,255,256,257,252,270,275,271,272,273,274,267,266,268,269,264,265,475,474,473,478,476,477,356,355,354,359,357,358,450,449,451,452,453,454,431,430,429,428,426,427,365,364,363,362,360,361,367,366,368,371,369,370,497,499,498,502,500,501,544,543,542,540,541,539,441,443,442,440,439,438,613,632,626,633,634,635,644,614,642,694,678,674,659,666,683,691,670,682,695,692,263,259,260,261,262,258,329,328,324,325,326,327,234,239,235,236,237,238,20,19,21,22,23,18,39,38,40,41,36,37,25,24,26,27,28,29,107,106,102,103,104,105,80,79,81,82,83,78,13,12,14,15,16,17,70,69,71,66,67,68,31,30,32,33,34,35,433,432,434,436,437,435,576,578,577,579,580,581,397,396,398,399,400,401,389,388,387,386,384,385,394,393,395,391,392,390,564,566,565,568,574,567,592,591,593,588,589,590,599,598,597,594,596,595,416,415,414,418,419,417,641,647,640,646,650,629,645,617,648,704,664,663,672,669,686,687,661,684,701,685,227,223,224,225,226,222,201,200,202,203,198,199,131,130,126,127,128,129,77,76,72,73,74,75,99,98,100,101,96,97,43,42,44,45,46,47,213,212,214,215,210,211,49,48,50,51,52,53,156,161,157,158,159,160,280,279,281,276,277,278,309,308,310,311,306,307,420,422,421,423,424,425,531,530,532,528,529,527,374,373,372,376,377,375,455,457,456,458,459,460,405,407,406,402,403,404,352,351,353,350,348,349,340,339,341,337,336,338,468,467,469,470,471,472,480,479,481,482,483,484,615,621,618,620,622,619,623,616,612,677,654,656,651,655,657,658,653,660,673,665 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#10604212f7d4a7b51fd21a22d9c743e5a67297285884dbf7fd2d260472af6645, M = {36, 37, 38, 39, 40, 41, 136} 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 21:53:49 · history