Equation 677 Database

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Magma fbc327491193…

magma fbc327491193
Size
705
Isomorphism class hash
fbc3274911937aa8437e78ebb5b6353180d604b6d2d6181dbb8f83a303282d48
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 20:36:53
Display reorder
660,541,481,123,175,389,542,482,176,124,390,540,480,125,177,388,484,544,122,174,392,485,545,120,172,393,483,543,121,173,391,487,547,129,181,395,488,548,130,182,396,486,546,131,183,394,550,490,128,180,398,551,491,126,178,399,549,489,127,179,397,670,672,664,667,307,327,246,329,297,308,325,330,244,295,309,326,245,328,296,323,306,249,332,293,324,304,247,333,294,322,305,248,331,292,318,313,252,335,303,316,314,250,336,301,317,315,251,334,302,312,321,255,338,299,310,319,253,339,300,311,320,254,337,298,685,686,689,688,17,445,48,505,205,15,446,506,49,206,16,444,50,504,207,448,13,51,508,204,449,14,52,509,202,447,12,53,507,203,451,23,54,511,196,452,21,55,512,197,450,22,56,510,198,19,454,57,514,199,20,455,58,515,200,18,453,59,513,201,669,668,662,666,401,66,77,601,529,402,67,602,75,530,400,68,76,600,528,69,404,73,604,532,70,405,74,605,533,71,403,72,603,531,64,407,83,607,535,65,408,81,608,536,63,406,82,606,534,410,60,79,610,538,411,61,80,611,539,409,62,78,609,537,675,682,678,681,413,377,221,577,353,414,378,578,222,354,412,376,220,576,352,380,416,224,580,356,381,417,225,581,357,379,415,223,579,355,383,419,227,583,359,384,420,228,584,360,382,418,226,582,358,422,386,230,586,362,423,387,231,587,363,421,385,229,585,361,665,671,661,663,188,457,38,565,621,189,458,566,36,622,187,456,37,564,620,460,184,41,568,624,461,185,39,569,625,459,186,40,567,623,463,194,44,571,627,464,195,42,572,628,462,193,43,570,626,190,466,47,574,630,191,467,45,575,631,192,465,46,573,629,693,698,700,695,150,614,132,152,437,148,615,153,133,438,149,613,134,151,436,617,146,135,155,440,618,147,136,156,441,616,145,137,154,439,612,144,138,158,443,647,645,139,644,646,619,159,140,157,442,652,655,141,653,654,656,659,142,657,658,649,651,143,648,650,703,702,701,704,267,269,237,469,341,265,270,470,235,342,266,268,236,468,340,272,263,233,472,344,273,264,234,473,345,271,262,232,471,343,275,258,243,475,347,276,256,241,476,348,274,257,242,474,346,261,278,239,478,350,259,279,240,479,351,260,277,238,477,349,699,696,694,697,365,101,214,493,553,366,99,494,215,554,364,100,216,492,552,97,368,217,496,556,98,369,218,497,557,96,367,219,495,555,107,371,212,499,559,105,372,213,500,560,106,370,211,498,558,374,103,208,502,562,375,104,209,503,563,373,102,210,501,561,674,676,680,684,170,286,24,633,517,171,287,634,25,518,169,288,26,632,516,289,166,27,636,520,290,167,28,637,521,291,168,29,635,519,284,161,30,639,523,285,162,31,640,524,283,160,32,638,522,164,280,33,642,526,165,281,34,643,527,163,282,35,641,525,679,683,677,673,425,589,0,114,93,426,590,115,2,94,424,588,1,116,95,592,428,4,117,92,593,429,5,118,90,591,427,3,119,91,595,431,7,112,84,596,432,8,113,85,594,430,6,111,86,434,598,10,108,87,435,599,11,109,88,433,597,9,110,89,687,692,691,690 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#c6a869941d5f836cd5f826f4a41a523fb37d651c2417bcc51f4579b275cefef3, 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 20:36:54 · history