Equation 677 Database

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Magma b9d9532872a5…

magma b9d9532872a5
Size
705
Isomorphism class hash
b9d9532872a51fa1f1b590bcab606e4da66d0613d864eabf3a83174295dca1e9
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 16:31:15
Display reorder
660,333,561,291,405,513,334,514,562,292,406,560,512,332,293,404,516,336,564,290,408,517,337,565,288,409,515,335,563,289,407,339,567,519,282,411,340,568,520,283,412,338,566,518,284,410,570,342,522,285,414,571,343,523,286,415,569,341,521,287,413,667,665,671,668,190,573,475,367,477,188,478,574,473,365,572,476,189,474,366,480,193,576,471,363,481,191,577,472,364,479,192,575,470,362,185,579,483,466,358,186,580,484,464,356,187,578,482,465,357,582,184,486,469,361,583,182,487,467,359,581,183,485,468,360,686,685,689,688,20,300,235,228,393,21,394,301,233,229,302,392,22,234,227,396,23,303,231,224,397,24,304,232,225,395,25,305,230,226,18,298,399,241,219,19,299,400,239,220,17,297,398,240,218,294,14,402,237,222,295,15,403,238,223,296,16,401,236,221,672,662,663,670,57,249,114,417,549,58,550,250,115,418,251,548,56,113,416,552,60,248,110,420,553,61,246,111,421,551,59,247,112,419,55,255,555,120,423,53,256,556,121,424,54,257,554,119,422,254,51,558,116,426,252,52,559,117,427,253,50,557,118,425,673,674,678,680,175,429,345,369,49,173,47,430,346,370,428,48,174,344,368,45,171,432,348,372,46,172,433,349,373,44,170,431,347,371,181,435,40,351,375,179,436,38,352,376,180,434,39,350,374,438,177,43,354,378,439,178,41,355,379,437,176,42,353,377,661,664,666,669,32,585,323,381,97,33,95,586,324,382,584,96,34,325,380,93,35,588,322,384,94,36,589,320,385,92,37,587,321,383,30,591,88,329,387,31,592,86,330,388,29,590,87,331,386,594,26,91,328,390,595,27,89,326,391,593,28,90,327,389,697,694,696,698,76,307,245,1,242,74,622,623,620,621,306,243,75,244,0,629,79,631,628,630,633,77,635,632,634,624,78,627,625,626,82,643,640,641,642,80,647,644,645,646,81,639,636,637,638,655,85,652,653,654,659,83,656,657,658,651,84,648,649,650,704,701,702,703,142,5,598,599,489,140,490,6,600,601,7,488,141,597,596,492,145,4,605,604,493,143,2,606,607,491,144,3,603,602,137,11,495,610,611,138,12,496,612,613,139,13,494,609,608,10,136,498,616,617,8,134,499,618,619,9,135,497,615,614,699,700,693,695,310,152,525,501,62,308,63,153,526,502,154,64,309,524,500,65,313,155,528,504,66,311,156,529,505,67,312,157,527,503,316,150,68,531,507,314,151,69,532,508,315,149,70,530,506,146,319,71,534,510,147,317,72,535,511,148,318,73,533,509,684,676,677,683,275,537,453,211,169,273,167,538,454,209,536,168,274,452,210,165,271,540,456,207,166,272,541,457,208,164,270,539,455,206,281,543,160,459,217,279,544,158,460,215,280,542,159,458,216,546,277,163,462,213,547,278,161,463,214,545,276,162,461,212,675,681,679,682,197,266,441,106,124,198,122,264,442,104,265,123,199,440,105,127,196,269,444,109,125,194,267,445,107,126,195,268,443,108,203,261,130,447,101,204,262,128,448,102,205,263,129,446,103,260,202,133,450,100,258,200,131,451,98,259,201,132,449,99,687,690,692,691 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#34588157c307db5531c4fa8d738de6f4f43dd6ced943a299dd02fbb5d9b36bf1, 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 16:31:16 · history