Equation 677 Database

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Magma d2339954078b…

magma d2339954078b
Size
705
Isomorphism class hash
d2339954078b4b35d452070905436f7911c95fdb134f4c3b3e61c7096bcc5947
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 17:33:25
Display reorder
660,261,443,210,467,455,211,262,468,456,444,209,442,260,466,454,264,206,446,470,458,207,265,447,471,459,208,263,445,469,457,201,267,441,465,453,202,268,439,463,451,200,266,440,464,452,270,204,437,461,449,271,205,438,462,450,460,269,203,436,448,666,667,665,668,377,357,44,282,352,42,378,283,350,358,43,356,379,281,351,376,47,360,278,355,45,374,361,279,353,46,375,359,280,354,39,368,363,273,347,40,369,364,274,348,41,370,362,272,349,371,38,366,276,346,372,36,367,277,344,275,373,37,365,345,690,687,686,688,227,479,195,411,551,196,228,412,552,480,194,478,229,410,550,226,198,482,414,554,199,224,483,415,555,197,225,481,413,553,193,233,477,409,549,191,234,475,407,547,192,235,476,408,548,232,189,473,405,545,230,190,474,406,546,404,231,188,472,544,672,664,669,671,296,292,102,181,515,100,297,179,516,290,101,291,298,180,514,299,105,295,177,518,103,300,293,178,519,104,301,294,176,517,108,302,287,187,513,106,303,288,185,511,107,304,289,186,512,305,111,286,183,509,306,109,284,184,510,182,307,110,285,508,678,680,677,675,387,503,72,319,399,73,388,317,400,504,71,502,386,318,398,390,68,506,315,402,69,391,507,316,403,70,389,505,314,401,78,385,501,310,397,79,383,499,308,395,77,384,500,309,396,381,74,497,313,393,382,75,498,311,394,312,380,76,496,392,663,662,670,661,431,213,157,587,575,158,432,588,576,214,159,212,430,586,574,434,156,216,590,578,154,435,217,591,579,155,433,215,589,577,148,429,219,585,573,149,427,220,583,571,150,428,218,584,572,425,151,222,581,569,426,152,223,582,570,580,424,153,221,568,696,697,693,694,635,423,143,99,61,144,647,646,645,644,142,422,634,98,60,655,146,652,653,654,147,659,656,657,658,145,651,649,648,650,141,633,417,97,64,139,631,418,95,62,140,632,416,96,63,629,137,420,93,67,630,138,421,94,65,92,628,136,419,66,701,702,703,704,611,527,321,161,169,322,612,636,637,528,320,526,610,160,168,614,324,530,641,640,325,615,531,643,642,323,613,529,638,639,327,609,525,164,175,328,607,523,162,173,326,608,524,163,174,605,330,521,167,171,606,331,522,165,172,166,604,329,520,170,700,699,695,698,256,491,8,599,563,6,254,600,564,492,7,490,255,598,562,259,11,494,602,566,9,257,495,603,567,10,258,493,601,565,3,251,489,597,561,4,252,487,595,559,5,253,488,596,560,250,2,485,593,557,248,1,486,594,558,592,249,0,484,556,681,682,676,684,340,50,119,539,623,120,338,540,624,48,118,49,339,538,622,343,122,53,542,626,123,341,51,543,627,121,342,52,541,625,117,335,56,537,621,115,336,54,535,619,116,337,55,536,620,334,113,59,533,617,332,114,57,534,618,532,333,112,58,616,683,679,673,674,87,33,236,131,16,237,88,132,17,34,238,35,86,130,15,90,239,32,134,12,240,91,30,135,13,241,89,31,133,14,242,85,24,129,22,243,83,25,127,23,244,84,26,128,21,81,245,27,125,18,82,246,28,126,19,124,80,247,29,20,689,685,691,692 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#58acf36cbe6044882516075a72a3c87dd19ad7333778c9b60a583a8d5c85fb41, 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 17:33:26 · history