Equation 677 Database

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Magma eb1cbc244bf4…

magma eb1cbc244bf4
Size
705
Isomorphism class hash
eb1cbc244bf44503b1c2d6c7c515aa49c381f9f7a970e8b4e6d63be92f884546
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 20:03:41
Display reorder
660,549,363,89,573,351,87,550,574,352,364,365,551,88,575,353,92,362,548,572,350,360,90,546,570,348,91,361,547,571,349,84,540,354,564,342,85,541,355,565,343,86,542,356,566,344,543,83,357,567,345,544,81,358,568,346,545,82,359,569,347,687,673,685,675,248,244,14,387,263,12,246,388,261,245,243,247,13,389,262,17,240,251,386,259,241,15,249,384,260,16,242,250,385,258,20,254,235,378,269,18,252,236,379,267,19,253,234,380,268,257,23,238,381,265,255,21,239,382,266,256,22,237,383,264,662,663,661,669,537,450,148,513,423,149,538,514,424,451,452,539,147,515,425,151,449,536,512,422,447,152,534,510,420,150,448,535,511,421,146,528,441,504,414,144,529,442,505,415,145,530,443,506,416,531,142,444,507,417,532,143,445,508,418,533,141,446,509,419,682,678,683,679,637,636,34,638,642,35,645,646,650,644,652,653,33,654,658,30,629,628,630,634,612,31,613,614,618,32,620,621,622,626,25,48,52,56,438,26,49,53,54,439,24,50,51,55,440,588,28,589,592,593,596,29,597,598,602,604,27,605,606,610,704,697,703,699,311,298,189,399,327,190,309,400,328,299,297,310,191,401,329,192,294,307,398,326,295,193,308,396,324,194,296,306,397,325,195,317,304,390,318,196,315,305,391,319,197,316,303,392,320,313,198,300,393,321,314,199,301,394,322,312,200,302,395,323,692,691,689,690,435,169,78,462,525,79,436,463,526,170,168,437,80,464,527,77,165,434,461,524,166,75,432,459,522,76,167,433,460,523,69,426,175,453,516,70,427,176,454,517,71,428,174,455,518,429,72,171,456,519,430,73,172,457,520,431,74,173,458,521,672,668,665,670,103,213,43,208,10,44,104,209,11,214,215,102,42,207,9,46,216,99,211,6,217,47,100,212,7,45,218,101,210,8,41,94,219,206,0,39,95,220,204,2,40,93,221,205,1,97,37,222,202,4,98,38,223,203,5,96,36,224,201,3,695,694,696,693,130,561,162,124,585,163,131,125,586,562,563,129,164,123,587,161,560,133,127,584,558,159,134,128,582,160,559,132,126,583,153,136,552,122,576,154,137,553,120,577,155,135,554,121,578,139,156,555,118,579,140,157,556,119,580,138,158,557,117,581,680,688,674,686,639,643,112,641,640,113,647,649,648,651,659,655,111,657,656,115,635,631,633,632,619,116,615,617,616,114,627,623,625,624,110,227,491,233,229,108,225,489,231,230,109,226,490,232,228,594,106,595,591,590,599,107,603,601,600,607,105,611,609,608,702,700,698,701,486,411,274,501,284,275,487,502,282,412,413,488,273,503,283,270,410,485,500,287,408,271,483,498,285,272,409,484,499,286,280,477,402,492,290,281,478,403,493,288,279,479,404,494,289,480,276,405,495,293,481,277,406,496,291,482,278,407,497,292,667,671,666,664,474,331,68,183,375,66,475,184,376,332,330,476,67,185,377,64,334,473,186,374,335,65,471,187,372,63,333,472,188,373,59,465,337,181,366,57,466,338,182,367,58,467,336,180,368,468,62,340,177,369,469,60,341,178,370,470,61,339,179,371,684,676,681,677 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#b88a5e69f4f2e8155017edd6b5c4ba2f90c1abf217fa4fb1e3b057bac30e1168, 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 20:03:42 · history