Equation 677 Database

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Magma 062f946ed0bb…

magma 062f946ed0bb
Size
707
Isomorphism class hash
062f946ed0bb803e5509a4d5e52caa7054c22b7ccbf7d5c3abf5d2456c35cf2c
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 08:21:08
Display reorder
513,515,514,511,512,510,646,166,162,167,163,165,164,118,117,119,114,115,116,78,83,79,80,81,82,43,42,44,45,46,47,73,72,74,75,76,77,172,171,173,169,168,170,184,183,185,180,181,182,293,280,281,279,291,292,287,286,282,283,284,285,175,174,176,177,178,179,124,123,125,120,121,122,602,601,603,605,585,586,446,445,444,449,447,448,338,337,336,340,341,339,439,438,440,441,442,443,456,458,457,461,459,460,382,381,383,379,380,378,415,414,416,418,419,417,427,426,428,429,430,431,572,571,570,573,574,575,626,628,632,606,633,627,629,630,631,687,691,654,668,695,706,704,703,699,705,698,278,275,273,274,277,276,254,253,249,250,251,252,272,271,267,268,269,270,260,259,255,256,257,258,264,263,265,266,261,262,14,13,15,16,17,12,3,2,4,5,1,0,91,90,92,93,94,95,52,51,53,48,49,50,71,70,66,67,68,69,54,59,55,56,57,58,359,358,357,355,356,354,364,363,365,361,362,360,564,566,565,569,567,568,392,391,390,394,395,393,518,517,516,520,521,519,400,399,401,397,398,396,536,535,534,539,537,538,592,591,590,587,589,588,547,546,548,551,549,550,622,635,620,640,624,636,621,610,625,670,697,659,656,674,688,693,694,667,685,679,26,29,27,28,25,24,20,19,21,22,23,18,97,96,98,99,100,101,211,210,207,206,208,209,36,41,37,38,39,40,203,202,204,201,200,205,196,195,197,198,199,194,290,289,247,248,187,186,288,246,242,243,244,245,108,113,109,110,111,112,192,191,193,188,189,190,600,604,599,578,576,577,582,584,583,579,580,581,424,423,425,420,421,422,436,435,437,432,433,434,353,352,351,349,350,348,388,387,389,385,386,384,332,331,330,335,333,334,454,453,455,450,451,452,596,598,597,593,595,594,617,611,615,616,618,612,623,614,613,676,701,661,660,680,692,700,675,681,682,677,224,227,225,226,229,228,218,223,219,220,221,222,212,217,213,214,215,216,237,236,238,239,240,241,235,234,230,231,232,233,65,64,60,61,62,63,6,11,7,8,9,10,150,155,151,152,153,154,161,160,156,157,158,159,104,103,105,106,107,102,88,87,89,84,85,86,413,412,411,409,410,408,553,552,554,556,557,555,522,524,523,527,525,526,372,374,373,377,375,376,369,371,370,368,366,367,541,540,542,544,545,543,529,528,530,532,533,531,561,563,562,560,558,559,407,406,405,402,403,404,641,637,607,638,634,639,609,619,608,696,686,655,684,678,690,702,683,673,689,669,328,324,329,325,327,326,144,149,145,146,147,148,309,308,310,311,307,306,323,322,319,318,320,321,31,30,32,33,34,35,305,304,301,300,302,303,137,136,132,133,134,135,128,127,129,130,131,126,141,140,142,143,138,139,314,312,315,316,317,313,299,298,295,294,296,297,506,505,504,508,509,507,463,462,464,466,467,465,503,502,501,499,500,498,491,490,489,487,488,486,482,481,480,484,485,483,347,346,345,344,342,343,473,472,471,470,468,469,477,479,478,476,474,475,493,492,494,497,495,496,643,651,645,648,647,644,642,650,649,664,671,652,653,666,665,672,663,657,662,658 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 = {102, 103, 104, 105, 106, 107, 134} 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 08:21:09 · history