Equation 677 Database

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Magma 2d55265aa379…

magma 2d55265aa379
Size
705
Isomorphism class hash
2d55265aa379b464d07aaa76d7d71186e89f74c0261a260e3ab90f5f32983ea9
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 21:45:58
Display reorder
660,444,441,449,271,453,272,461,464,469,473,420,270,428,431,434,504,274,501,509,513,524,275,520,529,533,484,273,481,489,493,560,565,269,571,576,580,585,267,591,596,540,545,268,551,556,621,625,265,631,636,645,641,266,651,656,605,601,264,611,616,687,689,695,692,452,451,446,255,445,256,471,472,466,465,423,257,433,430,429,512,254,511,506,505,532,252,531,526,525,492,253,491,486,485,574,575,261,567,566,594,595,262,587,586,554,555,263,547,546,634,635,260,627,626,655,654,258,647,646,615,614,259,607,606,701,698,703,685,84,361,374,236,349,234,362,85,376,350,360,235,86,372,348,87,239,364,381,352,88,237,365,382,353,89,238,363,379,351,367,90,231,387,355,368,91,232,389,356,366,92,233,385,354,370,93,230,393,358,94,371,228,395,359,95,369,229,390,357,682,679,673,676,409,325,113,154,375,155,326,410,111,377,324,153,408,112,373,412,150,328,109,380,413,151,329,110,383,411,152,327,108,378,331,415,145,119,386,332,416,146,117,388,330,414,144,118,384,334,418,148,115,392,419,335,149,116,394,417,333,147,114,391,684,667,678,670,456,450,458,241,457,242,470,476,478,477,432,240,436,438,437,517,244,510,518,516,538,245,530,539,537,497,243,490,498,496,572,561,247,573,570,592,581,248,593,590,552,541,246,553,550,632,620,250,633,630,640,652,251,653,650,600,612,249,613,610,686,688,699,696,440,459,442,123,454,124,479,460,462,474,439,125,426,425,435,500,122,519,502,514,521,120,536,522,534,480,121,499,482,494,579,562,129,563,577,599,582,130,583,597,559,542,131,543,557,639,622,128,623,637,642,659,126,643,657,602,619,127,603,617,691,702,697,704,448,443,455,21,447,22,463,468,475,467,427,23,422,424,421,508,20,503,515,507,528,18,523,535,527,488,19,483,495,487,564,569,12,578,568,584,589,13,598,588,544,549,14,558,548,624,629,15,638,628,649,644,16,658,648,609,604,17,618,608,694,700,690,693,78,337,220,47,0,45,338,79,221,2,336,46,80,219,1,81,43,340,216,4,82,44,341,217,5,83,42,339,218,3,343,76,38,226,7,344,77,36,227,8,342,75,37,225,6,346,72,41,222,10,73,347,39,223,11,74,345,40,224,9,669,681,668,671,178,138,277,99,164,100,139,179,278,162,140,101,177,276,163,174,98,141,280,167,175,96,142,281,165,176,97,143,279,166,136,169,105,283,159,137,170,106,284,160,135,168,107,282,161,132,172,104,286,158,173,133,102,287,156,171,134,103,285,157,661,663,672,662,397,288,301,61,187,62,289,398,302,188,290,60,396,300,186,400,64,291,304,190,401,65,292,305,191,399,63,293,303,189,294,403,67,307,185,295,404,68,308,183,296,402,66,306,184,297,406,70,310,181,407,298,71,311,182,405,299,69,309,180,683,664,675,680,313,192,204,51,35,52,193,314,205,33,194,53,312,206,34,316,50,195,207,31,317,48,196,208,32,315,49,197,209,30,198,319,57,210,26,199,320,58,211,24,200,318,59,212,25,201,322,56,213,29,323,202,54,214,27,321,203,55,215,28,665,677,666,674 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#f3708acaf97ab90d0e627f94c9229dfefc0b06412aed9a05696d0ed9b4a78cdc, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 21:45:59 · history