Equation 677 Database

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Magma 8261b76675f4…

magma 8261b76675f4
Size
705
Isomorphism class hash
8261b76675f46541ea03789cbc023868b270739de2628da53d94619de5bce07e
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 18:06:13
Display reorder
660,309,418,562,358,119,310,120,419,563,359,417,121,311,561,357,308,414,118,558,354,306,415,116,559,355,307,416,117,560,356,125,409,300,553,349,126,410,301,554,350,127,408,302,552,348,412,124,303,556,352,413,122,304,557,353,411,123,305,555,351,686,678,675,684,250,189,165,430,177,251,178,190,166,431,188,176,249,164,429,246,192,180,168,426,247,193,181,169,427,248,191,179,167,428,183,195,241,171,421,184,196,242,172,422,182,194,240,170,420,198,186,244,174,424,199,187,245,175,425,197,185,243,173,423,666,672,664,661,25,334,506,406,315,26,316,335,507,407,333,317,24,505,405,28,330,314,502,402,29,331,312,503,403,27,332,313,504,404,321,325,31,497,397,322,326,32,498,398,323,324,30,496,396,328,320,34,500,400,329,318,35,501,401,327,319,33,499,399,682,673,677,674,226,647,645,650,648,227,656,655,652,658,639,640,225,637,642,222,615,616,613,618,223,623,624,621,626,224,631,632,628,634,521,213,217,99,565,522,214,218,97,566,520,212,216,98,564,597,598,220,600,601,607,608,221,604,610,215,523,219,96,567,703,697,700,704,273,370,63,137,110,274,111,371,64,138,369,112,275,65,139,272,366,113,62,136,270,367,114,60,134,271,368,115,61,135,108,361,264,69,128,109,362,265,70,129,107,360,266,71,130,364,104,267,68,131,365,105,268,66,132,363,106,269,67,133,692,690,689,693,43,202,346,51,518,44,519,200,347,52,201,517,42,345,53,46,205,514,342,50,47,203,515,343,48,45,204,516,344,49,509,208,41,337,57,510,206,39,338,58,508,207,40,336,59,211,512,37,340,56,209,513,38,341,54,210,511,36,339,55,662,667,670,669,1,284,84,141,21,0,22,282,85,142,283,23,2,86,140,3,287,20,87,144,4,285,18,88,145,5,286,19,89,143,12,279,6,90,147,13,280,7,91,148,14,281,8,92,146,278,15,9,93,150,276,16,10,94,151,277,17,11,95,149,691,695,696,694,298,594,582,466,550,299,551,595,583,467,593,549,297,581,465,294,590,546,578,462,295,591,547,579,463,296,592,548,580,464,541,585,289,573,457,542,586,290,574,458,540,584,288,572,456,588,544,292,576,460,589,545,293,577,461,587,543,291,575,459,687,688,680,685,158,644,651,646,649,159,657,653,659,654,636,641,160,643,638,161,612,617,619,614,162,620,625,627,622,163,629,633,635,630,537,102,156,569,482,538,103,157,570,480,536,101,155,568,481,602,603,152,599,596,605,609,153,611,606,100,539,154,571,483,701,698,702,699,234,454,494,262,394,235,395,455,495,263,453,393,236,493,261,237,450,390,490,258,238,451,391,491,259,239,452,392,492,260,385,445,232,485,253,386,446,233,486,254,384,444,231,484,252,448,388,228,488,256,449,389,229,489,257,447,387,230,487,255,668,665,671,663,78,534,478,442,382,79,383,535,479,443,533,381,80,477,441,81,530,378,474,438,82,531,379,475,439,83,532,380,476,440,373,525,76,469,433,374,526,77,470,434,372,524,75,468,432,528,376,72,472,436,529,377,73,473,437,527,375,74,471,435,681,683,679,676 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#62d5cd0053185ccae094f96e2ae535daccc2dacd55a9f14470e4ff2a7e2e534c, 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 18:06:14 · history