Equation 677 Database

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Magma 1fb66c258417…

magma 1fb66c258417
Size
705
Isomorphism class hash
1fb66c258417eb6a157ea03174816627215e10b772251f35c4a0ec1a105f1b64
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 21:19:16
Display reorder
660,282,511,382,488,272,283,383,486,270,509,284,510,384,487,271,491,381,281,514,268,379,279,512,489,269,380,280,513,490,267,388,517,273,494,263,389,515,274,492,261,390,516,275,493,262,520,387,276,497,266,518,385,277,495,264,519,386,278,496,265,673,678,674,677,252,140,2,160,243,253,1,161,244,138,254,139,0,159,245,156,5,251,143,246,3,249,141,157,247,4,250,142,158,248,8,135,258,166,241,6,136,259,167,242,7,137,260,165,240,134,11,257,162,237,132,9,255,163,238,133,10,256,164,239,671,664,670,665,476,181,91,172,403,474,92,173,404,182,475,180,90,171,405,168,94,479,184,406,95,477,185,169,407,93,478,183,170,408,89,187,482,178,409,87,188,480,179,410,88,186,481,177,411,190,85,485,174,412,191,86,483,175,413,189,84,484,176,414,676,687,682,684,209,358,75,350,500,207,76,348,498,356,208,357,77,349,499,346,74,212,361,503,72,210,359,347,501,73,211,360,345,502,81,364,204,354,506,82,362,205,352,504,83,363,206,353,505,654,80,653,656,657,365,78,343,355,507,366,79,344,351,508,703,697,704,698,453,570,289,393,99,451,290,391,100,568,452,569,288,392,101,396,285,456,573,98,286,454,571,394,96,287,455,572,395,97,295,576,459,399,105,296,574,457,397,106,294,575,458,398,107,579,291,462,402,104,577,292,460,400,102,578,293,461,401,103,692,693,694,690,419,192,52,429,558,420,53,427,556,193,418,194,51,428,557,432,48,415,195,561,49,416,196,430,559,50,417,197,431,560,58,198,425,435,564,59,199,426,433,562,57,200,424,434,563,201,54,421,438,567,202,55,422,436,565,203,56,423,437,566,661,663,667,662,63,46,21,126,316,64,22,127,317,47,65,45,23,128,315,129,20,62,42,319,18,60,43,130,320,19,61,44,131,318,12,37,69,124,314,13,38,70,125,312,14,36,71,123,313,40,15,68,120,310,41,16,66,121,311,39,17,67,122,309,695,691,696,689,594,642,367,441,618,592,368,439,616,640,593,641,369,440,617,444,370,597,645,621,371,595,643,442,619,372,596,644,443,620,373,648,600,447,624,374,646,598,445,622,375,647,599,446,623,651,376,603,450,627,649,377,601,448,625,650,378,602,449,626,683,688,685,675,326,547,25,334,465,324,26,332,463,545,325,546,24,333,464,337,28,322,550,468,29,323,548,335,466,27,321,549,336,467,31,553,330,340,471,32,551,328,338,469,30,552,329,339,470,659,34,658,652,655,554,35,331,341,472,555,33,327,342,473,699,701,700,702,219,606,154,229,535,220,155,230,533,604,221,605,153,228,534,225,150,222,609,538,151,223,607,226,536,152,224,608,227,537,145,612,217,235,541,146,610,218,236,539,144,611,216,234,540,615,148,213,231,544,613,149,214,232,542,614,147,215,233,543,672,669,666,668,116,582,305,523,630,114,303,521,628,580,115,581,304,522,629,526,308,119,585,633,306,117,583,524,631,307,118,584,525,632,300,588,111,529,636,301,586,112,527,634,302,587,113,528,635,591,299,110,532,639,589,297,108,530,637,590,298,109,531,638,680,681,686,679 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#e6ff3ea71fab369083c7c0ebcc1e5818a214c988729d733a41fa2a4b44566c90, 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 21:19:17 · history