Equation 677 Database

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Magma 821130f361df…

magma 821130f361df
Size
707
Isomorphism class hash
821130f361dfaf924203cafdfb5f025aafdfd0e2c2b217b8afa6bb3d63248fda
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
2026-10-08 21:25:43
Display reorder
559,558,560,561,562,563,636,31,33,34,35,30,32,268,267,269,265,264,266,196,195,197,192,193,194,358,357,359,355,354,356,183,182,184,185,180,181,330,331,332,333,334,335,119,118,114,115,116,117,154,153,155,150,151,152,258,263,259,260,261,262,278,277,279,280,281,276,285,284,286,287,282,283,343,340,344,345,338,339,410,409,408,413,411,412,555,557,556,552,553,554,566,565,564,568,569,567,493,492,494,496,497,495,525,527,526,522,523,524,515,514,513,510,511,512,502,501,503,498,499,500,423,425,424,422,420,421,614,613,615,616,617,628,627,629,696,662,652,670,654,672,702,697,689,704,706,705,18,20,21,22,23,19,272,271,273,274,275,270,342,341,353,350,351,349,303,302,304,305,300,301,233,232,228,229,230,231,99,98,100,101,96,97,49,48,50,51,52,53,215,214,210,211,212,213,46,45,47,42,43,44,1,5,0,2,3,4,208,207,209,204,205,206,104,103,105,106,107,102,594,595,596,598,599,597,384,386,385,387,388,389,376,375,377,372,373,374,593,592,591,590,589,588,441,443,442,438,439,440,444,446,445,448,449,447,457,456,458,459,460,461,378,380,379,383,381,382,631,630,632,625,633,623,626,624,699,651,676,659,657,663,690,679,675,684,703,700,68,70,71,66,67,69,108,113,109,110,111,112,27,26,28,29,24,25,148,147,149,144,145,146,81,80,82,83,78,79,122,121,123,124,125,120,186,191,187,188,189,190,243,242,244,245,240,241,77,76,72,73,74,75,296,295,297,298,299,294,315,314,316,317,312,313,310,309,311,306,307,308,418,417,419,415,416,414,365,364,363,362,361,360,428,427,426,430,431,429,368,367,366,371,369,370,508,507,509,505,506,504,533,532,531,528,529,530,581,580,579,576,578,577,516,518,517,521,519,520,606,611,610,609,612,607,621,622,686,668,677,661,647,666,681,691,680,692,695,694,255,257,252,253,254,256,251,250,246,247,248,249,336,337,352,347,348,346,57,56,58,59,54,55,291,290,292,293,288,289,217,216,218,219,220,221,93,92,94,95,90,91,63,62,64,65,60,61,84,89,85,86,87,88,226,225,227,222,223,224,36,41,37,38,39,40,199,198,200,201,202,203,602,604,603,600,601,605,403,402,404,406,407,405,586,585,587,583,582,584,451,450,452,454,455,453,465,467,466,462,463,464,432,434,433,436,437,435,392,391,390,394,395,393,397,396,398,399,400,401,634,619,620,635,643,644,618,608,685,674,655,678,649,669,683,688,664,687,701,698,162,164,165,166,167,163,127,126,128,129,130,131,10,9,11,6,7,8,157,156,158,159,160,161,139,138,140,141,142,143,173,172,168,169,170,171,12,17,13,14,15,16,329,328,325,324,326,327,235,234,236,237,238,239,321,320,322,323,319,318,179,178,174,175,176,177,137,136,132,133,134,135,536,535,534,539,537,538,545,544,543,542,540,541,468,470,469,473,471,472,489,491,490,486,487,488,548,547,546,551,549,550,571,570,572,575,573,574,482,481,480,484,485,483,479,478,477,475,476,474,637,639,640,642,641,638,646,645,682,650,660,656,648,653,667,671,658,665,693,673 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#10604212f7d4a7b51fd21a22d9c743e5a67297285884dbf7fd2d260472af6645, M = {114, 115, 116, 117, 118, 119, 128} 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 2026-10-08 21:25:44 · history