Equation 677 Database

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Magma 555e3520c450…

magma 555e3520c450
Size
705
Isomorphism class hash
555e3520c450842c606aa90760b7dcb0aa4e985993d85abe6e952381a8ef2a51
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 16:53:06
Display reorder
660,20,293,623,432,563,18,433,294,624,564,19,434,295,625,565,23,292,431,622,562,21,290,429,620,560,22,291,430,621,561,614,299,15,423,554,615,300,16,424,555,616,301,17,425,556,298,617,14,426,557,296,618,12,427,558,297,619,13,428,559,671,664,667,670,205,360,171,575,168,203,576,361,172,169,204,577,362,170,167,201,359,574,174,164,202,357,572,175,165,200,358,573,173,166,177,351,196,566,159,178,352,194,567,160,176,353,195,568,158,354,180,199,569,162,355,181,197,570,163,356,179,198,571,161,690,688,685,686,54,229,408,240,635,52,241,227,409,636,53,239,228,410,637,50,225,236,407,634,51,226,237,405,632,49,224,238,406,633,399,220,45,231,626,400,218,43,232,627,401,219,44,230,628,223,402,48,234,629,221,403,46,235,630,222,404,47,233,631,663,662,672,668,7,182,611,587,420,8,588,183,612,421,6,589,184,613,422,10,185,586,610,419,11,186,584,608,417,9,187,585,609,418,602,188,5,578,411,603,189,3,579,412,604,190,4,580,413,191,605,0,581,414,192,606,2,582,415,193,607,1,583,416,682,681,676,678,144,599,456,539,372,145,540,600,457,373,143,541,601,458,374,140,598,538,455,371,141,596,536,453,369,142,597,537,454,370,447,590,135,530,363,448,591,136,531,364,449,592,134,532,365,593,450,138,533,366,594,451,139,534,367,595,452,137,535,368,665,666,661,669,216,488,444,512,527,217,513,489,445,528,215,514,490,446,529,212,491,515,443,526,213,492,516,441,524,214,493,517,442,525,435,486,207,510,518,436,487,208,511,519,437,485,206,509,520,482,438,210,506,521,483,439,211,507,522,484,440,209,508,523,695,697,698,696,131,647,481,477,112,132,654,655,652,653,133,656,659,657,658,130,646,478,98,113,128,644,479,99,114,129,645,480,97,115,93,638,122,475,120,91,639,123,476,121,92,640,124,474,119,641,96,125,471,116,642,94,126,472,117,643,95,127,473,118,703,702,701,704,105,396,36,308,83,103,648,397,649,84,104,650,398,651,82,101,395,309,312,79,102,393,310,313,80,100,394,311,314,81,42,387,111,306,89,40,388,109,307,90,41,389,110,305,88,390,38,107,302,85,391,39,108,303,86,392,37,106,304,87,700,699,693,694,74,146,384,503,278,75,504,147,385,279,73,505,148,386,280,77,149,502,383,281,78,150,500,381,282,76,151,501,382,283,375,152,72,494,284,376,153,70,495,285,377,154,71,496,286,155,378,68,497,287,156,379,69,498,288,157,380,67,499,289,675,677,673,680,25,315,551,331,348,26,332,316,552,349,24,330,317,553,350,28,318,327,550,347,29,319,328,548,345,27,320,329,549,346,542,321,31,337,339,543,322,32,338,340,544,323,30,336,341,324,545,34,333,342,325,546,35,334,343,326,547,33,335,344,679,683,674,684,62,248,468,264,266,63,265,249,469,267,61,263,250,470,268,65,251,260,467,269,66,252,261,465,270,64,253,262,466,271,459,246,60,255,272,460,247,58,256,273,461,245,59,254,274,242,462,56,258,275,243,463,57,259,276,244,464,55,257,277,687,689,692,691 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#458b3cfe489c9903ffdf95802569f7fced83cfa9f913419e94bc2fd3ec4c05bf, 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 16:53:09 · history