Equation 677 Database

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Magma b9c408fe8e5b…

magma b9c408fe8e5b
Size
720
Isomorphism class hash
b9c408fe8e5b61b4b664818b955a4b3cdaa36036d7ec24b287007c46d748fd1b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 719) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 23:50:44
Display reorder
541,542,543,544,545,546,547,548,549,550,551,552,553,554,540,719,131,109,156,132,110,157,133,111,158,134,112,159,120,113,160,121,114,161,122,115,162,123,116,163,124,117,164,125,118,150,126,119,151,127,105,152,128,106,153,129,107,154,155,130,108,139,146,147,148,149,135,136,137,138,141,142,143,144,145,140,690,688,689,687,352,331,326,353,332,327,354,333,328,355,334,329,356,335,315,357,336,316,358,337,317,359,338,318,345,339,319,346,340,320,347,341,321,348,342,322,349,343,323,350,344,324,325,351,330,309,301,302,303,304,305,306,307,308,311,312,313,314,300,310,681,682,680,679,34,28,171,35,29,172,36,15,173,37,16,174,38,17,175,39,18,176,40,19,177,41,20,178,42,21,179,43,22,165,44,23,166,30,24,167,31,25,168,32,26,169,170,33,27,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,700,702,699,701,583,562,611,584,563,612,570,564,613,571,565,614,572,566,600,573,567,601,574,568,602,575,569,603,576,555,604,577,556,605,578,557,606,579,558,607,580,559,608,581,560,609,610,582,561,592,599,585,586,587,588,589,590,591,594,595,596,597,598,593,716,717,715,718,450,445,425,451,446,426,452,447,427,453,448,428,454,449,429,455,435,430,456,436,431,457,437,432,458,438,433,459,439,434,460,440,420,461,441,421,462,442,422,463,443,423,424,464,444,473,465,466,467,468,469,470,471,472,475,476,477,478,479,474,704,706,703,705,260,240,286,261,241,287,262,242,288,263,243,289,264,244,290,265,245,291,266,246,292,267,247,293,268,248,294,269,249,295,255,250,296,256,251,297,257,252,298,258,253,299,285,259,254,284,276,277,278,279,280,281,282,283,271,272,273,274,275,270,678,676,677,675,536,514,508,537,515,509,538,516,495,539,517,496,525,518,497,526,519,498,527,520,499,528,521,500,529,522,501,530,523,502,531,524,503,532,510,504,533,511,505,534,512,506,507,535,513,491,483,484,485,486,487,488,489,490,493,494,480,481,482,492,709,708,710,707,183,233,211,184,234,212,185,235,213,186,236,214,187,237,215,188,238,216,189,239,217,190,225,218,191,226,219,192,227,220,193,228,221,194,229,222,180,230,223,181,231,224,210,182,232,208,200,201,202,203,204,205,206,207,195,196,197,198,199,209,696,698,695,697,630,623,11,631,624,12,632,625,13,633,626,14,634,627,1,635,628,0,636,629,2,637,615,3,638,616,4,639,617,5,640,618,6,641,619,7,642,620,8,643,621,9,10,644,622,653,645,646,647,648,649,650,651,652,655,656,657,658,659,654,712,713,714,711,408,401,380,409,402,381,410,403,382,411,404,383,412,390,384,413,391,385,414,392,386,415,393,387,416,394,388,417,395,389,418,396,375,419,397,376,405,398,377,406,399,378,379,407,400,363,370,371,372,373,374,360,361,362,365,366,367,368,369,364,685,684,686,683,78,72,51,79,73,52,80,74,53,81,60,54,82,61,55,83,62,56,84,63,57,85,64,58,86,65,59,87,66,45,88,67,46,89,68,47,75,69,48,76,70,49,50,77,71,102,94,95,96,97,98,99,100,101,104,90,91,92,93,103,691,693,692,694 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 720 = 16 + 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#9916b9303e5777c051d457f13e65b220048127e3f9475b765d37bfd24fd4df83, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 58, 75} 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 2026-10-08 23:50:45 · history