Equation 677 Database

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Magma 9291b44e4b35…

magma 9291b44e4b35
Size
707
Isomorphism class hash
9291b44e4b3562e51e835ed6fd7292161217a89131cefadbafc47c2a7242be7c
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 16:36:08
Display reorder
540,542,541,543,544,545,638,19,21,22,23,18,20,251,250,246,247,248,249,8,7,9,10,11,6,356,354,357,358,359,355,129,128,130,131,126,127,335,334,330,331,332,333,185,184,180,181,182,183,293,292,288,289,290,291,167,166,162,163,164,165,315,314,316,317,312,313,273,272,274,275,270,271,343,340,344,345,338,339,474,476,475,477,478,479,416,415,414,419,417,418,501,503,502,500,498,499,552,554,553,555,556,557,457,456,458,461,459,460,431,430,429,427,428,426,548,547,546,550,551,549,409,408,410,411,412,413,633,634,631,632,630,629,622,628,694,671,660,665,650,679,702,700,684,704,706,705,91,93,94,95,90,92,52,51,53,48,49,50,341,342,353,350,346,351,328,327,329,326,325,324,211,210,212,213,214,215,223,222,224,225,226,227,157,156,158,159,160,161,207,206,208,209,204,205,323,322,319,318,320,321,193,192,194,195,196,197,201,200,202,203,198,199,98,97,99,100,101,96,559,560,558,561,562,563,480,482,481,483,484,485,371,370,369,367,368,366,388,387,389,385,386,384,362,360,361,363,364,365,382,381,383,378,379,380,512,511,510,514,515,513,582,583,584,585,586,587,606,611,609,610,608,607,626,625,696,658,676,657,651,669,688,677,678,689,703,695,39,41,36,37,38,40,301,300,302,303,304,305,3,2,4,5,1,0,31,30,32,33,34,35,170,169,171,172,173,168,176,175,177,178,179,174,135,134,136,137,132,133,26,25,27,28,29,24,89,88,84,85,86,87,219,218,220,221,216,217,44,43,45,46,47,42,54,59,55,56,57,58,524,523,522,527,525,526,575,574,573,572,571,570,403,402,404,405,406,407,400,399,401,397,398,396,530,529,528,531,532,533,535,534,536,537,538,539,505,504,506,507,508,509,567,569,568,566,565,564,614,615,617,616,613,635,621,612,687,670,675,662,648,663,692,683,673,681,697,699,106,102,103,104,105,107,115,114,116,117,118,119,336,337,352,348,349,347,189,188,190,191,186,187,154,153,155,150,151,152,142,141,143,138,139,140,149,148,144,145,146,147,113,112,108,109,110,111,14,13,15,16,17,12,74,73,75,76,77,72,66,71,67,68,69,70,64,63,65,60,61,62,441,443,442,438,439,440,453,455,454,450,451,452,576,577,578,579,580,581,374,373,372,377,375,376,520,519,521,518,516,517,593,592,591,588,590,589,390,392,391,395,393,394,437,436,435,433,434,432,618,619,620,623,643,644,624,627,691,680,659,672,647,664,690,693,661,682,701,698,238,234,235,236,237,239,278,277,279,280,281,276,78,83,79,80,81,82,266,265,267,268,269,264,260,259,261,262,263,258,285,284,286,287,282,283,124,123,125,120,121,122,255,254,256,257,252,253,308,307,309,310,311,306,298,297,299,294,295,296,242,241,243,244,245,240,232,231,233,228,229,230,602,600,601,605,603,604,472,471,473,469,470,468,493,492,494,495,496,497,467,466,465,464,462,463,425,424,423,420,421,422,449,448,447,445,446,444,596,594,595,598,599,597,488,487,486,490,491,489,636,642,637,641,639,640,645,646,685,653,652,656,649,654,667,668,655,666,686,674 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 = {90, 91, 92, 93, 94, 95, 133} 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 16:36:10 · history