Equation 677 Database

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Magma c64071179950…

magma c64071179950
Size
705
Isomorphism class hash
c6407117995011b382479a1096454c94109062dec3214c3590b1212c4c8bfa7e
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 20:07:48
Display reorder
660,169,463,557,533,320,170,531,461,555,321,168,532,462,556,322,529,172,459,553,323,530,173,460,554,324,528,171,458,552,325,548,454,175,524,326,546,452,176,522,327,547,453,174,523,328,457,551,178,527,329,455,549,179,525,330,456,550,177,526,331,684,682,673,678,194,70,56,237,254,192,238,71,54,252,193,239,69,55,253,240,197,66,59,250,241,195,67,57,251,242,196,68,58,249,51,61,200,235,245,52,62,198,236,243,53,60,199,234,244,64,50,203,231,248,65,48,201,232,246,63,49,202,233,247,665,670,661,664,17,579,78,497,129,15,495,577,79,130,16,496,578,80,131,493,13,575,81,128,494,14,576,82,126,492,12,574,83,127,76,570,23,488,120,77,568,21,486,121,75,569,22,487,122,573,72,19,491,123,571,73,20,489,124,572,74,18,490,125,687,679,680,686,152,652,653,654,658,150,638,636,637,642,151,646,644,645,650,622,155,620,621,626,630,153,629,628,634,614,154,612,613,618,211,206,147,217,560,209,207,148,215,558,210,208,149,216,559,605,604,146,608,609,205,212,144,218,561,204,213,145,214,562,704,698,700,703,102,184,339,379,267,103,377,185,340,268,104,378,183,338,269,375,105,180,342,270,376,106,181,343,271,374,107,182,341,272,337,190,100,370,273,335,191,101,368,274,336,189,99,369,275,186,333,96,373,276,187,334,97,371,277,188,332,98,372,278,689,690,692,694,139,509,415,591,396,140,589,507,413,397,138,590,508,414,395,587,142,505,411,392,588,143,506,412,393,586,141,504,410,394,406,500,137,582,402,404,498,135,580,403,405,499,136,581,401,503,409,133,585,398,501,407,134,583,399,502,408,132,584,400,663,672,666,668,347,427,109,284,292,348,282,425,110,293,349,283,426,108,291,280,346,423,112,295,281,344,424,113,296,279,345,422,111,294,115,418,353,290,298,116,416,354,288,299,114,417,355,289,297,421,118,352,286,301,419,119,350,287,302,420,117,351,285,300,693,695,696,691,4,521,545,603,42,5,601,519,543,43,3,602,520,544,44,599,1,517,541,45,600,0,518,542,46,598,2,516,540,47,536,512,10,594,40,534,510,11,592,41,535,511,9,593,39,515,539,6,597,36,513,537,7,595,37,514,538,8,596,38,683,688,685,681,309,655,657,659,656,310,643,639,641,640,311,651,647,649,648,627,312,623,625,624,635,313,631,633,632,619,314,615,617,616,471,317,307,565,466,469,315,308,563,464,470,316,306,564,465,610,611,303,607,606,318,472,304,566,467,319,473,305,567,468,702,701,697,699,85,265,367,485,222,86,483,266,365,223,84,484,264,366,224,481,88,261,363,221,482,89,262,364,219,480,87,263,362,220,358,256,91,476,228,356,257,92,474,229,357,255,90,475,230,259,361,94,479,227,260,359,95,477,225,258,360,93,478,226,662,667,669,671,157,432,391,451,28,158,449,433,389,29,156,450,431,390,27,447,160,428,387,24,448,161,429,388,25,446,159,430,386,26,382,438,163,442,34,380,439,164,440,35,381,437,162,441,33,434,385,166,445,30,435,383,167,443,31,436,384,165,444,32,676,677,674,675 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#ba7c5b5fc3c8b2f23fa53f03c835320f8b0f039ca1c741e1670481476e08a637, 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 20:07:49 · history