Equation 677 Database

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Magma 5d1533907374…

magma 5d1533907374
Size
705
Isomorphism class hash
5d15339073742a95bea40f799a42aa4fe5530a4aa9c474f4ca65d2bda4913632
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 17:39:04
Display reorder
660,399,527,394,423,326,400,528,327,392,424,398,526,328,393,422,402,530,329,397,426,403,531,330,395,427,401,529,331,396,425,389,405,533,332,429,406,534,333,390,430,404,532,334,391,428,536,408,335,388,432,537,409,336,386,433,535,407,337,387,431,680,678,682,674,258,50,239,573,9,259,48,10,240,574,257,49,11,241,572,254,53,8,238,576,255,51,6,236,577,256,52,7,237,575,245,249,56,1,579,250,54,0,246,580,248,55,2,247,578,59,252,3,244,582,57,253,4,242,583,58,251,5,243,581,666,669,672,661,447,82,411,197,28,448,83,29,412,198,446,81,27,410,196,450,78,24,414,200,451,79,25,415,201,449,80,26,413,199,417,453,73,34,195,454,74,35,418,193,452,72,33,416,194,76,456,30,420,191,77,457,31,421,192,75,455,32,419,190,677,673,675,681,308,507,186,218,207,309,508,205,184,219,310,506,206,185,217,311,510,203,189,214,312,511,204,187,215,313,509,202,188,216,181,306,513,213,222,307,514,211,182,223,305,512,212,183,221,646,645,209,648,649,657,656,210,652,653,515,304,208,180,220,704,698,700,703,179,459,597,346,265,177,460,263,598,344,178,458,264,596,345,175,462,261,600,349,176,463,262,601,347,174,461,260,599,348,603,170,465,271,341,168,466,269,604,342,169,464,270,602,343,468,173,267,606,340,469,171,268,607,338,467,172,266,605,339,694,689,690,692,471,495,96,539,135,472,496,136,97,540,470,494,137,98,538,474,498,134,99,542,475,499,132,100,543,473,497,133,101,541,102,477,501,141,545,478,502,142,103,546,476,500,143,104,544,504,480,140,105,548,505,481,138,106,549,503,479,139,107,547,662,667,665,663,119,129,166,356,272,117,130,273,167,357,118,131,274,165,358,115,128,275,162,359,116,126,276,163,360,114,127,277,164,361,157,110,120,278,354,108,121,279,158,355,109,122,280,156,353,123,113,281,160,350,124,111,282,161,351,125,112,283,159,352,691,695,696,693,363,435,585,633,88,364,436,89,586,634,362,434,87,584,632,366,438,84,588,636,367,439,85,589,637,365,437,86,587,635,591,369,441,94,639,370,442,95,592,640,368,440,93,590,638,444,372,90,594,642,445,373,91,595,643,443,371,92,593,641,685,688,679,676,564,290,296,517,41,562,288,39,294,518,563,289,40,295,516,567,293,37,299,520,565,291,38,297,521,566,292,36,298,519,302,570,285,47,523,568,286,45,300,524,569,287,46,301,522,650,651,43,644,647,654,659,44,655,658,284,571,42,303,525,697,701,702,699,551,234,483,621,71,552,235,69,484,622,550,233,70,482,620,554,230,67,486,624,555,231,68,487,625,553,232,66,485,623,489,557,225,62,627,558,226,60,490,628,556,224,61,488,626,228,560,65,492,630,229,561,63,493,631,227,559,64,491,629,664,671,670,668,609,19,146,379,317,610,20,318,144,377,608,18,319,145,378,612,22,316,149,375,613,23,314,147,376,611,21,315,148,374,152,615,17,323,385,616,15,324,150,383,614,16,325,151,384,13,618,322,155,381,14,619,320,153,382,12,617,321,154,380,686,684,683,687 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#5c1fa523b4d9d2fbb415708ccaff34546079d57eeb66e712dcba93d7172179c8, 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 17:39:05 · history