Equation 677 Database

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Magma 6392ae84e7c1…

magma 6392ae84e7c1
Size
705
Isomorphism class hash
6392ae84e7c1e60278b14b0df6da1c5cd490378f66d2cee7ab7d68d089dc1cb1
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 21:55:27
Display reorder
660,121,345,515,86,354,346,84,122,513,355,347,85,120,514,356,124,89,344,511,357,125,87,342,512,358,123,88,343,510,359,351,119,521,81,360,352,117,519,82,361,353,118,520,83,362,115,350,517,80,363,116,348,518,78,364,114,349,516,79,365,669,672,662,667,527,162,312,263,133,163,261,525,313,134,164,262,526,314,132,523,259,165,315,136,524,260,166,316,137,522,258,167,317,135,168,533,310,269,131,169,531,311,267,129,170,532,309,268,130,529,171,306,265,127,530,172,307,266,128,528,173,308,264,126,689,691,687,685,419,57,479,111,33,58,112,417,477,35,59,113,418,478,31,415,110,56,475,38,416,108,54,476,41,414,109,55,474,36,63,425,485,102,45,64,423,483,103,47,65,424,484,104,42,421,62,481,105,51,422,60,482,106,53,420,61,480,107,48,670,664,661,666,139,407,443,180,467,405,181,140,441,465,406,182,138,442,466,142,183,403,439,463,143,184,404,440,464,141,185,402,438,462,413,145,449,178,473,411,146,447,179,471,412,144,448,177,472,148,409,445,174,469,149,410,446,175,470,147,408,444,176,468,676,678,682,677,581,431,629,187,455,429,188,579,627,453,430,186,580,628,454,577,190,427,625,451,578,191,428,626,452,576,189,426,624,450,437,587,635,193,461,435,585,633,194,459,436,586,634,192,460,583,433,631,196,457,584,434,632,197,458,582,432,630,195,456,663,665,668,671,100,395,605,23,371,393,21,101,603,369,394,22,99,604,370,96,19,391,601,367,97,20,392,602,368,98,18,390,600,366,401,91,611,29,377,399,92,609,27,375,400,90,610,28,376,94,397,607,25,373,95,398,608,26,374,93,396,606,24,372,695,694,693,699,572,550,12,52,4,551,49,570,13,5,549,50,571,14,3,568,44,546,11,7,569,46,547,9,8,567,43,548,10,6,656,659,657,34,658,651,650,648,30,649,652,655,653,32,654,574,552,17,40,0,575,553,15,37,2,573,554,16,39,1,701,703,704,702,272,560,286,201,539,558,202,270,287,537,559,203,271,285,538,275,200,556,282,535,273,198,557,283,536,274,199,555,284,534,566,278,292,207,545,564,276,293,208,543,565,277,291,209,544,281,562,288,206,541,279,563,289,204,542,280,561,290,205,540,697,696,700,698,383,246,244,341,503,247,339,381,245,501,248,340,382,243,502,379,337,249,240,499,380,338,250,241,500,378,336,251,242,498,252,389,235,332,509,253,387,236,330,507,254,388,234,331,508,385,255,238,335,505,386,256,239,333,506,384,257,237,334,504,673,679,674,684,593,217,157,305,641,218,303,591,158,639,216,304,592,156,640,589,301,220,160,637,590,302,221,161,638,588,300,219,159,636,215,599,155,296,647,213,597,153,294,645,214,598,154,295,646,595,211,151,299,643,596,212,152,297,644,594,210,150,298,642,680,683,681,675,617,491,326,68,230,489,66,615,324,228,490,67,616,325,229,613,71,487,329,233,614,69,488,327,231,612,70,486,328,232,497,623,321,74,225,495,621,322,72,226,496,622,323,73,227,619,493,320,77,224,620,494,318,75,222,618,492,319,76,223,686,690,692,688 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#fbd23cd98406f165f23d6b41307d902a92b7e2e110ccd89116da4983a4804a48, 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 21:55:28 · history