Equation 677 Database

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Magma 0be56891eca6…

magma 0be56891eca6
Size
705
Isomorphism class hash
0be56891eca68e8c2bb824cf3f0464a274f435144d5c39de46372b18edd98f4d
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 21:11:26
Display reorder
660,153,333,345,357,369,151,334,346,358,370,152,347,359,371,335,156,348,336,360,372,154,349,337,361,373,155,350,338,362,374,159,351,339,363,375,364,157,352,340,376,158,353,341,365,377,354,162,342,366,378,355,160,343,367,379,356,161,344,368,380,685,686,688,687,207,453,467,439,441,205,454,465,440,442,206,466,438,443,455,210,470,456,435,444,208,468,457,436,445,209,469,458,437,446,202,473,459,430,447,431,203,471,460,448,204,472,461,429,449,476,201,462,433,450,474,199,463,434,451,475,200,464,432,452,701,702,704,703,328,615,631,142,11,329,616,629,143,12,327,630,144,13,614,331,627,618,141,10,332,628,619,139,8,330,626,617,140,9,326,622,613,148,17,149,324,620,611,18,325,621,612,150,19,625,322,609,147,16,623,323,610,145,14,624,321,608,146,15,670,669,672,671,216,261,102,484,499,214,262,100,485,500,215,101,483,498,263,212,98,264,487,495,213,99,265,488,496,211,97,266,486,497,222,93,267,482,490,480,220,91,268,491,221,92,269,481,489,96,218,270,478,493,94,219,271,479,494,95,217,272,477,492,680,677,679,678,224,277,509,518,529,225,278,507,516,530,223,508,517,528,276,227,512,273,514,525,228,510,274,515,526,226,511,275,513,527,230,504,283,524,535,522,231,505,284,536,229,506,282,523,534,503,233,279,520,531,501,234,280,521,532,502,232,281,519,533,689,690,691,692,301,64,242,111,591,302,62,243,109,592,300,241,110,593,63,297,245,67,114,594,298,246,65,112,595,299,244,66,113,596,307,240,59,106,589,107,308,238,60,590,306,239,61,108,588,236,303,58,105,585,237,304,56,103,586,235,305,57,104,587,697,698,700,699,37,639,655,21,48,35,640,653,22,44,36,654,20,46,638,39,651,642,24,54,40,652,643,25,51,42,650,641,23,52,45,646,637,27,38,28,47,644,635,41,49,645,636,26,43,649,50,633,30,34,647,53,634,31,32,648,55,632,29,33,661,662,664,663,383,185,120,68,170,381,186,118,69,171,382,119,70,169,184,386,116,181,71,173,384,117,182,72,174,385,115,183,73,172,389,126,176,74,168,75,387,124,177,166,388,125,175,76,167,122,392,179,77,164,123,390,180,78,165,121,391,178,79,163,682,681,684,683,316,5,603,250,81,317,6,604,251,82,315,602,252,83,7,319,606,4,249,84,320,607,2,247,85,318,605,3,248,86,314,601,0,256,87,257,312,600,1,80,313,658,657,656,659,598,310,258,255,88,599,311,259,253,89,597,309,260,254,90,693,694,696,695,294,575,547,551,571,295,573,548,549,572,296,546,550,570,574,293,543,578,554,567,291,544,576,552,568,292,545,577,553,569,285,538,581,557,562,555,286,539,579,563,287,537,580,556,561,541,288,584,560,565,542,289,582,558,566,540,290,583,559,564,666,665,668,667,135,416,421,190,400,133,414,422,191,401,134,420,192,399,415,138,417,412,189,403,136,418,413,187,404,137,419,411,188,402,130,427,407,196,398,197,131,428,405,396,132,426,406,198,397,423,129,410,195,394,424,127,408,193,395,425,128,409,194,393,674,673,676,675 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#dcedbe28d6e821630efaff61054e89b4af79513af364c6246d7e9f07a2213221, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 21:11:27 · history