Equation 677 Database

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Magma 5ff844e79dc1…

magma 5ff844e79dc1
Size
705
Isomorphism class hash
5ff844e79dc13921ca5f6c6ea0bf08a93828243338c40da0d8d7fecaf9f6ea9b
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 20:03:05
Display reorder
660,102,207,69,393,202,100,200,208,67,394,206,201,101,68,392,210,105,205,65,396,211,103,203,66,397,64,209,104,204,395,108,75,197,213,391,106,73,198,214,389,107,74,199,212,390,71,111,196,216,387,72,109,194,217,388,70,110,195,215,386,672,665,663,666,173,97,343,623,361,174,359,98,341,624,99,360,175,342,622,96,172,357,339,626,94,170,358,340,627,338,95,171,356,625,179,349,352,88,621,180,347,350,89,619,181,348,351,90,620,345,178,355,91,617,346,176,353,92,618,344,177,354,93,616,690,685,689,686,257,84,333,455,467,258,468,82,334,456,83,466,259,332,454,87,256,470,336,458,85,254,471,337,459,335,86,255,469,457,263,331,465,79,453,264,329,463,80,451,265,330,464,81,452,327,262,461,78,449,328,260,462,76,450,326,261,460,77,448,667,661,664,668,186,278,293,115,369,187,370,279,294,116,280,368,185,295,117,281,182,372,292,114,282,183,373,290,112,291,283,184,371,113,192,299,367,284,121,193,300,365,285,122,191,301,366,286,123,298,188,363,287,120,296,189,364,288,118,297,190,362,289,119,674,678,673,677,46,8,398,515,503,47,504,9,399,516,7,502,48,400,514,4,49,506,401,518,5,50,507,402,519,403,6,51,505,517,44,404,501,14,513,45,405,499,15,511,43,406,500,13,512,407,40,497,10,509,408,41,498,11,510,409,42,496,12,508,669,671,670,662,59,226,551,539,491,60,492,224,552,540,225,490,58,550,538,229,62,494,554,542,227,63,495,555,543,553,228,61,493,541,57,549,489,221,537,55,547,487,222,535,56,548,488,223,536,545,53,485,220,533,546,54,486,218,534,544,52,484,219,532,695,697,696,693,274,635,131,1,139,272,646,647,644,645,634,138,273,130,0,655,277,654,652,653,659,275,658,656,657,648,651,276,650,649,269,129,145,633,133,270,127,143,631,134,271,128,144,632,132,125,268,141,629,136,126,266,142,630,137,124,267,140,628,135,701,703,702,704,34,575,3,417,422,35,636,576,637,418,574,429,36,2,416,578,37,640,641,420,579,38,642,643,421,639,577,39,638,419,32,431,428,573,415,33,432,426,571,413,31,430,427,572,414,434,28,424,569,411,435,29,425,570,412,433,30,423,568,410,699,700,694,698,169,563,381,479,527,167,528,564,382,480,562,526,168,380,478,566,165,530,384,482,567,166,531,385,483,383,565,164,529,481,160,379,525,561,477,158,377,523,559,475,159,378,524,560,476,375,163,521,557,473,376,161,522,558,474,374,162,520,556,472,679,675,684,680,253,319,443,587,611,251,612,317,444,588,318,610,252,442,586,315,249,614,446,590,316,250,615,447,591,445,314,248,613,589,244,441,609,325,585,242,439,607,323,583,243,440,608,324,584,437,247,605,321,581,438,245,606,322,582,436,246,604,320,580,682,676,681,683,233,599,309,150,18,234,16,600,310,151,598,17,235,308,149,602,232,21,312,146,603,230,19,313,147,311,601,231,20,148,239,307,24,597,156,240,305,22,595,157,241,306,23,596,155,303,238,27,593,152,304,236,25,594,153,302,237,26,592,154,687,688,691,692 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#b87a44718af64d04bd4c9a05b8565b67306fb6d5f63754d3fbad663d9bf67702, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 20:03:06 · history