Equation 677 Database

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Magma 8d8b4f500817…

magma 8d8b4f500817
Size
705
Isomorphism class hash
8d8b4f500817df91a87da6d297b292db06b5049cc3062e1a8240acae28e943c2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 17:37:14
Display reorder
660,49,381,513,477,561,50,382,514,478,562,383,479,48,515,563,52,380,512,476,560,378,53,510,474,558,51,379,511,475,559,504,55,372,468,552,505,56,373,469,553,506,54,374,470,554,58,507,375,471,555,59,508,376,472,556,57,509,377,473,557,679,686,676,682,286,525,333,313,194,287,526,334,314,192,527,312,285,335,193,282,524,332,316,190,522,283,330,317,191,284,523,331,315,189,324,277,516,319,200,325,278,517,320,198,326,276,518,318,199,280,327,519,322,196,281,328,520,323,197,279,329,521,321,195,667,669,670,663,82,393,537,141,309,83,394,538,142,310,395,143,81,539,311,78,392,536,144,308,390,79,534,145,306,80,391,535,146,307,528,73,384,147,300,529,74,385,148,301,530,72,386,149,302,76,531,387,150,303,77,532,388,151,304,75,533,389,152,305,678,673,677,684,16,636,637,643,640,17,644,645,651,648,652,659,15,653,656,12,629,628,635,632,612,13,613,619,616,14,620,621,627,624,97,22,139,467,446,98,23,140,465,444,96,21,138,466,445,18,588,589,593,592,19,597,598,603,600,20,605,606,611,608,700,697,703,704,40,229,219,429,405,41,230,220,430,406,228,431,39,221,407,36,225,222,428,404,226,37,223,426,402,38,227,224,427,403,217,46,235,420,396,218,47,236,421,397,216,45,234,422,398,42,213,231,423,399,43,214,232,424,400,44,215,233,425,401,691,690,692,689,153,357,344,549,462,154,358,342,550,463,359,551,155,343,464,156,356,347,548,461,354,157,345,546,459,158,355,346,547,460,339,159,348,540,453,340,160,349,541,454,341,161,350,542,455,162,338,351,543,456,163,336,352,544,457,164,337,353,545,458,671,668,664,661,267,70,132,582,583,268,71,133,584,585,69,587,269,134,586,270,66,131,580,581,67,271,129,577,576,272,68,130,579,578,123,265,61,171,170,124,266,62,172,168,125,264,60,173,169,261,126,64,174,166,262,127,65,175,167,263,128,63,176,165,696,695,694,693,24,369,573,501,489,25,370,574,502,490,371,503,26,575,491,27,368,572,500,488,366,28,570,498,486,29,367,571,499,487,564,30,360,492,480,565,31,361,493,481,566,32,362,494,482,33,567,363,495,483,34,568,364,496,484,35,569,365,497,485,681,680,675,687,182,641,638,639,642,180,649,646,647,650,657,655,181,654,658,178,633,630,631,634,617,179,614,615,618,177,625,622,623,626,137,188,449,273,450,135,186,447,274,451,136,187,448,275,452,184,594,595,590,591,185,596,601,599,602,183,604,609,607,610,702,699,698,701,204,441,297,417,84,205,442,298,418,85,443,419,206,299,86,203,440,296,416,87,438,201,294,414,88,202,439,295,415,89,288,210,432,408,90,289,211,433,409,91,290,212,434,410,92,209,291,435,411,93,207,292,436,412,94,208,293,437,413,95,665,672,666,662,103,245,2,113,259,104,243,1,111,260,244,112,102,0,258,99,248,5,116,255,246,100,3,114,256,101,247,4,115,257,8,109,240,119,250,6,110,241,117,251,7,108,242,118,249,105,11,239,122,253,106,9,237,120,254,107,10,238,121,252,683,674,688,685 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#5aa74a2d4b4bbe4036558963ef968fca94fa5f577bdbfbf2823cea2791e8d20b, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 17:37:17 · history