Equation 677 Database

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Magma af4bfe43a391…

magma af4bfe43a391
Size
707
Isomorphism class hash
af4bfe43a391af386db3dcb860ed80e2b88161fbc5bce42346f0312f741a219a
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 13:31:24
Display reorder
91,94,92,93,90,95,706,120,125,121,122,123,124,13,12,14,15,16,17,184,183,185,180,181,182,254,253,255,256,257,252,177,176,178,179,174,175,137,136,132,133,134,135,18,23,19,20,21,22,29,28,24,25,26,27,195,194,196,197,192,193,220,219,221,216,217,218,603,588,605,601,597,599,592,591,590,566,564,565,541,540,542,543,544,545,463,462,464,465,466,467,306,307,308,309,310,311,511,510,509,514,512,513,550,549,548,546,547,551,501,500,502,498,499,497,406,405,407,402,403,404,554,552,553,555,556,557,626,623,624,616,629,618,617,620,621,622,697,696,673,684,704,698,705,701,703,699,159,158,160,161,156,157,276,281,277,278,279,280,246,251,247,248,249,250,273,272,274,275,270,271,153,152,154,155,150,151,53,52,48,49,50,51,5,4,1,0,2,3,210,215,211,212,213,214,209,208,204,205,206,207,68,67,69,70,71,66,528,527,529,530,531,532,526,525,524,523,521,522,327,329,328,326,324,325,486,485,487,488,489,490,321,323,322,320,318,319,382,381,383,379,380,378,520,519,518,515,516,517,584,582,583,587,585,586,450,452,451,455,453,454,372,374,373,376,377,375,640,639,637,641,635,643,644,615,614,636,693,702,671,666,689,678,695,680,677,676,8,7,9,10,11,6,144,149,145,146,147,148,263,262,259,258,260,261,40,39,41,36,37,38,32,31,33,34,35,30,169,168,170,171,172,173,268,267,269,265,264,266,128,127,129,130,131,126,187,186,188,189,190,191,244,243,245,240,241,242,602,589,604,600,596,598,595,573,593,594,574,575,344,343,342,346,347,345,409,408,410,411,412,413,338,337,336,340,341,339,391,390,392,394,395,393,397,396,398,401,399,400,388,387,389,385,386,384,506,508,507,505,503,504,317,316,315,312,313,314,627,607,625,619,628,606,613,612,611,609,687,700,665,664,679,685,691,686,672,692,291,290,292,293,288,289,62,61,63,64,65,60,202,201,203,198,199,200,225,224,226,227,222,223,237,236,238,239,234,235,231,230,232,233,228,229,58,57,59,54,55,56,42,47,43,44,45,46,287,286,283,282,284,285,143,142,138,139,140,141,478,477,476,539,475,474,334,333,335,331,332,330,371,370,369,367,368,366,570,572,571,569,568,567,460,459,461,456,457,458,445,444,446,448,449,447,470,469,468,471,472,473,580,579,581,576,578,577,482,484,483,481,479,480,561,558,562,559,560,563,634,632,633,642,631,630,638,610,608,645,690,694,667,668,682,675,688,683,674,681,97,96,98,99,100,101,89,88,84,85,86,87,113,112,108,109,110,111,295,299,294,296,297,298,302,300,303,304,305,301,83,82,78,79,80,81,167,166,162,163,164,165,102,107,103,104,105,106,73,72,74,75,76,77,116,115,117,118,119,114,440,439,438,442,443,441,358,357,359,355,356,354,534,533,535,536,537,538,422,421,420,424,425,423,417,419,418,416,414,415,428,427,426,431,429,430,436,435,437,434,432,433,348,350,349,351,352,353,491,493,492,496,494,495,362,361,360,363,364,365,646,655,649,652,651,648,647,654,650,653,660,669,656,657,661,662,670,659,658,663 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#92768bb2ce71adf5f3645437d2daad1854a25afcd5bf6e7bdc519de5c37f97ae, M = {0, 1, 2, 3, 4, 5, 146} 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 13:31:25 · history