Equation 677 Database

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Magma c8650df60ee2…

magma c8650df60ee2
Size
705
Isomorphism class hash
c8650df60ee2892956a8e95ace89e66789b3b45a0a11dc526e82cf18f67d46c2
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 16:40:34
Display reorder
704,476,440,486,452,474,438,487,450,439,451,475,488,443,479,489,455,477,441,490,453,478,442,491,454,471,435,484,447,472,436,485,448,473,437,483,449,434,470,480,446,432,468,481,444,433,469,482,445,462,463,464,465,466,467,460,461,458,456,457,459,702,703,700,701,656,659,658,657,648,651,650,649,655,653,652,654,643,641,642,640,645,647,646,644,637,639,638,636,621,623,622,620,613,615,614,612,617,619,618,616,635,633,634,632,627,624,626,625,631,629,630,628,6,7,8,9,10,11,4,5,2,1,0,3,691,689,688,690,275,221,279,244,273,219,280,245,220,243,274,281,217,271,278,240,272,218,276,241,270,216,277,242,266,227,285,250,264,225,286,251,265,226,287,249,223,269,284,246,224,267,282,247,222,268,283,248,252,253,254,255,256,257,258,259,263,261,262,260,672,674,675,673,346,26,351,362,347,24,352,360,25,361,345,353,29,342,350,365,343,27,348,363,344,28,349,364,337,32,357,368,338,30,358,366,336,31,359,367,35,340,356,371,33,341,354,369,34,339,355,370,382,383,381,378,379,380,373,374,375,376,377,372,681,683,682,680,182,96,201,167,180,97,202,165,98,166,181,203,99,185,200,163,183,100,198,164,184,101,199,162,188,102,192,158,186,103,193,156,187,104,194,157,105,191,195,161,106,189,196,159,107,190,197,160,173,171,172,169,170,168,179,177,174,175,176,178,693,692,695,694,415,15,421,392,416,16,422,390,17,391,414,420,14,418,424,395,419,12,425,393,417,13,423,394,413,21,427,387,411,22,428,388,412,23,426,389,20,409,430,386,18,410,431,384,19,408,429,385,402,403,404,405,406,407,400,401,398,396,397,399,698,697,696,699,576,501,593,563,577,502,591,561,503,562,578,592,500,579,589,559,580,498,590,560,581,499,588,558,582,492,599,554,583,493,597,552,584,494,598,553,495,585,595,557,496,586,596,555,497,587,594,556,568,569,567,564,565,566,574,575,572,570,571,573,687,685,686,684,119,212,123,132,117,210,124,133,211,134,118,125,215,115,122,135,116,213,120,136,114,214,121,137,110,207,129,138,108,208,130,139,109,209,131,140,206,113,128,141,204,111,126,142,205,112,127,143,148,149,147,144,145,146,154,155,152,150,151,153,661,663,662,660,316,236,325,289,317,234,326,290,235,288,315,324,239,312,328,292,313,237,329,293,314,238,327,291,322,231,331,295,323,232,332,296,321,233,330,294,230,318,334,298,228,319,335,299,229,320,333,297,309,310,311,308,306,307,300,301,305,303,304,302,676,678,679,677,95,40,48,64,93,41,49,65,39,63,94,50,36,91,51,60,92,37,52,61,90,38,53,62,86,46,54,70,84,47,55,71,85,45,56,69,42,89,57,66,43,87,58,67,44,88,59,68,72,73,74,75,76,77,78,79,83,81,82,80,664,666,667,665,528,603,545,515,529,604,543,513,605,514,530,544,602,531,541,511,532,600,542,512,533,601,540,510,534,609,551,506,535,610,549,504,536,611,550,505,608,537,547,509,606,538,548,507,607,539,546,508,520,521,519,516,517,518,526,527,524,522,523,525,670,671,668,669 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#38a4e23a99caaa7b44b0fde217361d7389ff59fad772c7ae239f5a60818fe03a, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 16:40:37 · history