Equation 677 Database

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Magma a64985300fb2…

magma a64985300fb2
Size
705
Isomorphism class hash
a64985300fb2b4b62994c6eeaf361a63918717a2ab08134eb256422ec3b57620
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 20:37:38
Display reorder
660,464,181,231,77,602,232,182,75,600,462,463,180,233,76,601,184,467,230,73,605,185,465,228,74,603,183,466,229,72,604,459,187,237,68,597,66,460,188,238,598,461,186,239,67,599,190,458,236,71,596,191,456,234,69,594,189,457,235,70,595,664,665,671,672,351,248,19,590,370,20,246,588,371,352,353,247,18,589,369,251,350,22,593,366,249,348,23,591,367,250,349,21,592,368,357,243,17,585,361,586,358,244,15,362,359,245,16,587,360,242,356,13,584,364,240,354,14,582,365,241,355,12,583,363,690,689,686,688,560,214,28,428,32,24,215,426,35,558,559,213,26,427,30,210,563,34,431,25,211,561,31,429,27,212,562,33,430,29,555,205,40,423,45,424,556,206,37,47,557,204,38,425,42,208,554,46,422,36,209,552,43,420,39,207,553,44,421,41,661,670,667,663,404,257,578,374,512,576,255,372,510,402,403,256,577,373,511,253,407,581,377,515,254,405,579,375,513,252,406,580,376,514,399,263,573,380,507,378,400,261,574,508,401,262,575,379,509,259,398,572,383,506,260,396,570,381,504,258,397,571,382,505,682,674,678,673,536,264,392,548,313,390,265,546,314,534,535,266,391,547,312,267,539,395,551,316,268,537,393,549,317,269,538,394,550,315,531,270,387,543,319,544,532,271,388,320,533,272,389,545,318,273,530,386,542,322,274,528,384,540,323,275,529,385,541,321,662,668,666,669,199,79,440,5,452,438,80,3,450,200,198,78,439,4,451,82,202,443,0,455,83,203,441,2,453,81,201,442,1,454,197,85,435,11,447,9,195,86,436,448,196,84,437,10,449,88,193,434,7,446,89,194,432,8,444,87,192,433,6,445,694,697,695,693,645,65,644,647,646,638,63,639,637,636,641,64,640,643,642,61,657,656,659,658,62,648,649,651,650,60,652,653,655,654,107,56,565,621,52,622,105,54,566,53,106,55,564,623,51,59,103,568,620,48,57,104,569,618,49,58,102,567,619,50,702,701,703,704,500,327,629,290,628,624,328,288,625,498,499,329,627,289,626,326,503,635,293,634,324,501,631,291,630,325,502,633,292,632,495,333,284,296,281,294,496,334,282,279,497,335,283,295,280,332,494,287,299,277,330,492,285,297,278,331,493,286,298,276,700,696,699,698,154,91,168,524,158,169,92,522,156,155,153,90,170,523,157,94,150,171,527,161,95,151,172,525,159,93,152,173,526,160,145,97,174,519,164,520,146,98,175,162,144,96,176,521,163,100,148,177,518,167,101,149,178,516,165,99,147,179,517,166,680,683,676,679,346,310,416,614,476,414,311,612,474,347,345,309,415,613,475,306,342,419,617,479,307,343,417,615,477,308,344,418,616,478,337,301,411,609,471,610,338,302,412,472,336,300,413,611,473,304,340,410,608,470,305,341,408,606,468,303,339,409,607,469,675,681,677,684,136,222,113,125,488,111,223,123,486,137,135,224,112,124,487,225,132,109,121,491,226,133,110,122,489,227,134,108,120,490,142,220,119,131,483,129,143,221,117,484,141,219,118,130,485,216,138,115,127,482,217,139,116,128,480,218,140,114,126,481,685,692,687,691 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#c6bb22b65ea8da42821d53c407d340f5ca33ab54805c0683c0d4385c20756f88, 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 20:37:39 · history