Equation 677 Database

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Magma 63f492cf9807…

magma 63f492cf9807
Size
705
Isomorphism class hash
63f492cf980706afb3c7a1a8ee41aa404dd5c187ef1fa88cb48942a87139f753
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 16:53:51
Display reorder
660,490,346,442,381,280,491,443,382,278,344,489,345,441,380,279,349,493,445,384,283,347,494,446,385,281,348,492,444,383,282,440,341,379,488,286,342,438,377,486,284,343,439,378,487,285,340,436,375,484,289,338,437,376,485,287,483,339,435,374,288,676,683,682,679,0,234,466,101,81,2,467,99,82,235,1,233,465,100,83,230,21,469,97,80,231,15,470,98,78,232,20,468,96,79,464,240,107,4,72,241,462,105,5,73,239,463,106,3,74,236,460,103,7,75,237,461,104,8,76,6,238,459,102,77,667,665,672,666,527,243,298,321,111,528,296,322,112,244,526,242,297,320,113,246,530,301,324,110,247,531,299,325,108,245,529,300,323,109,293,249,319,525,117,250,294,317,523,118,248,295,318,524,119,252,292,315,521,116,253,290,316,522,114,520,251,291,314,115,673,674,685,677,622,93,621,623,626,630,628,631,634,94,614,95,613,615,618,92,646,645,647,650,90,654,653,655,658,91,638,637,639,642,604,84,607,606,610,85,589,591,590,594,86,596,599,598,602,87,573,574,576,577,88,582,583,580,586,227,89,202,229,544,698,702,704,703,357,136,169,406,394,358,167,407,395,137,356,135,168,405,393,132,360,172,409,397,133,361,170,410,398,134,359,171,408,396,175,142,404,355,392,143,173,402,353,390,141,174,403,354,391,138,178,400,351,388,139,176,401,352,389,350,140,177,399,387,692,691,690,694,120,256,369,218,309,121,370,219,310,254,122,255,368,220,308,259,123,372,217,312,257,124,373,215,313,258,125,371,216,311,367,262,224,126,307,260,365,225,127,305,261,366,226,128,306,265,363,223,129,303,263,364,221,130,304,131,264,362,222,302,661,662,670,663,70,156,185,194,148,71,186,195,146,157,69,155,187,193,147,159,66,188,191,144,160,67,189,571,570,158,68,190,192,145,183,162,197,61,154,163,184,198,62,152,161,182,196,60,153,165,179,200,64,150,166,180,201,65,151,63,164,181,199,149,695,696,693,689,333,46,565,478,539,334,566,479,540,47,332,45,564,477,538,42,336,568,481,542,43,337,569,482,543,44,335,567,480,541,563,37,476,331,537,38,561,474,329,535,36,562,475,330,536,40,559,472,327,533,41,560,473,328,534,326,39,558,471,532,681,686,675,687,625,52,624,627,620,633,632,635,629,53,617,51,616,619,612,48,649,648,651,644,49,657,656,659,652,50,641,640,643,636,608,58,611,609,605,59,592,595,593,588,57,600,603,601,597,54,578,579,575,572,55,584,587,585,581,495,56,386,545,228,699,700,701,697,209,12,553,515,418,210,554,516,419,13,211,14,552,514,417,11,212,556,518,421,9,213,557,519,422,10,214,555,517,420,551,16,513,207,416,19,549,511,208,414,23,550,512,206,415,17,547,509,203,412,18,548,510,204,413,205,22,546,508,411,669,664,668,671,268,26,503,454,430,266,504,455,431,24,267,25,502,453,429,29,271,506,457,433,27,269,507,458,434,28,270,505,456,432,501,32,452,274,428,30,499,450,272,426,31,500,451,273,427,35,497,448,277,424,33,498,449,275,425,276,34,496,447,423,680,678,688,684 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#47b26c2e0558f6c4fdff38c956d09d23d3aef780160b6fe0856dd3e8f07caf34, 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 16:53:53 · history