Equation 677 Database

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Magma 5c683953ae59…

magma 5c683953ae59
Size
705
Isomorphism class hash
5c683953ae59dd4f9359991e024056ccfc822341c28cc70bee1058f16991ddab
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 15:29:00
Display reorder
660,201,270,207,216,458,202,271,208,217,456,203,272,209,218,457,273,200,206,219,461,274,198,204,220,459,275,199,205,221,460,268,192,213,222,453,269,193,214,223,454,267,194,215,224,455,195,264,212,225,452,196,265,210,226,450,197,266,211,227,451,661,668,672,670,333,175,446,46,614,334,176,444,42,612,335,174,445,44,613,178,332,449,38,617,179,330,447,41,615,177,331,448,37,616,173,339,441,47,609,171,340,442,43,610,172,341,443,45,611,338,169,440,39,608,336,170,438,40,606,337,168,439,24,607,690,689,685,687,560,239,470,302,125,558,237,468,300,123,559,238,469,301,124,235,563,473,305,121,236,561,471,303,122,234,562,472,304,120,230,555,465,297,131,228,556,466,298,129,229,557,467,299,130,554,233,464,296,127,552,231,462,294,128,553,232,463,295,126,662,666,671,669,343,32,590,524,434,344,33,588,522,432,342,31,589,523,433,35,346,593,527,437,36,347,591,525,435,34,345,592,526,436,30,349,585,519,429,28,350,586,520,430,29,348,587,521,431,352,26,584,518,428,353,27,582,516,426,351,25,583,517,427,679,675,673,682,422,13,386,374,362,420,14,384,372,360,421,12,385,373,361,16,425,389,377,365,17,423,387,375,363,15,424,388,376,364,11,417,381,369,357,9,418,382,370,358,10,419,383,371,359,416,7,380,368,356,414,8,378,366,354,415,6,379,367,355,664,663,667,665,410,109,94,548,286,408,110,95,546,287,409,108,93,547,285,112,413,90,551,282,113,411,91,549,283,111,412,92,550,284,115,405,85,543,277,116,406,86,544,278,114,407,84,545,276,404,118,88,542,280,402,119,89,540,281,403,117,87,541,279,698,693,694,695,646,56,647,644,645,638,54,639,636,637,642,55,643,640,641,59,658,659,656,657,57,650,651,648,649,58,654,655,652,653,51,581,621,489,4,52,579,622,490,5,53,580,623,491,3,577,50,620,488,1,578,48,618,486,0,576,49,619,487,2,702,701,703,704,628,68,313,629,512,624,66,314,625,510,626,67,312,627,511,71,634,316,635,515,69,631,317,630,513,70,633,315,632,514,63,289,311,18,507,64,290,309,19,508,65,288,310,20,509,292,62,307,21,506,293,60,308,22,504,291,61,306,23,505,700,696,699,697,500,154,602,261,186,498,155,600,262,187,499,153,601,263,188,150,503,605,260,189,151,501,603,258,190,152,502,604,259,191,145,495,597,252,184,146,496,598,253,185,144,497,599,254,183,494,148,596,255,180,492,149,594,256,181,493,147,595,257,182,676,680,678,683,161,82,482,572,328,159,83,480,570,329,160,81,481,571,327,78,157,485,575,324,79,158,483,573,325,80,156,484,574,326,73,167,477,567,319,74,165,478,568,320,72,166,479,569,318,163,76,476,566,322,164,77,474,564,323,162,75,475,565,321,681,674,684,677,398,104,536,248,136,396,102,534,246,137,397,103,535,247,135,107,401,539,251,132,105,399,537,249,133,106,400,538,250,134,99,393,531,243,142,100,394,532,244,143,101,395,533,245,141,392,98,530,242,138,390,96,528,240,139,391,97,529,241,140,688,691,686,692 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#19ea6a1480a1f5a2ac1b5eeb32448a05ed8c6404ec648162b4da66f77bce13ec, 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 15:29:01 · history