Equation 677 Database

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Magma eeb58a7e1d3e…

magma eeb58a7e1d3e
Size
705
Isomorphism class hash
eeb58a7e1d3ec52c7f303db45156fff21e6257c33ef349a1095e3208dafc18f8
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 16:54:02
Display reorder
660,371,130,271,427,475,372,272,428,476,131,370,129,270,426,474,126,374,274,430,478,127,375,275,431,479,128,373,273,429,477,277,136,425,369,473,137,278,423,367,471,135,276,424,368,472,132,280,421,365,469,133,281,422,366,470,364,134,279,420,468,666,667,661,664,583,98,245,250,595,584,243,251,596,96,582,97,244,249,594,101,586,241,246,598,99,587,242,247,599,100,585,240,248,597,236,93,256,581,593,94,234,257,579,591,95,235,255,580,592,92,239,252,577,589,90,237,253,578,590,576,91,238,254,588,685,691,690,687,318,59,333,395,383,319,334,396,384,57,320,58,335,394,382,55,321,332,398,386,56,322,330,399,387,54,323,331,397,385,339,65,393,324,381,63,340,391,325,379,64,341,392,326,380,61,338,389,327,377,62,336,390,328,378,329,60,337,388,376,665,663,669,668,463,202,451,354,157,464,452,352,158,203,462,201,450,353,156,198,466,454,357,160,199,467,455,355,161,200,465,453,356,159,449,208,360,461,155,209,447,358,459,153,207,448,359,460,154,204,445,363,457,151,205,446,361,458,152,456,206,444,362,150,677,673,678,676,547,163,535,148,559,548,536,149,560,164,546,162,534,147,558,166,550,538,144,562,167,551,539,145,563,165,549,537,146,561,533,169,139,545,557,170,531,140,543,555,168,532,138,544,556,172,529,142,541,553,173,530,143,542,554,540,171,528,141,552,662,672,671,670,499,178,12,288,81,500,13,289,82,179,498,177,14,290,83,174,502,15,291,80,175,503,16,292,78,176,501,17,293,79,18,184,286,497,87,185,19,287,495,88,183,20,285,496,89,180,21,282,493,86,181,22,283,494,84,492,182,23,284,85,693,698,696,694,407,228,349,351,643,647,645,646,644,229,406,230,348,350,642,231,654,652,653,655,232,658,657,656,659,233,650,648,649,651,347,226,52,401,637,227,345,53,402,638,225,346,51,400,636,222,343,48,404,640,223,344,49,405,641,403,224,342,50,639,702,703,704,701,523,29,194,487,619,524,192,488,620,27,522,28,193,486,618,25,526,197,490,622,26,527,195,491,623,24,525,196,489,621,189,35,485,521,617,33,190,483,519,615,34,191,484,520,616,31,188,481,517,613,32,186,482,518,614,516,30,187,480,612,695,700,697,699,115,259,511,439,103,116,512,440,104,260,114,258,510,438,102,262,118,514,442,106,263,119,515,443,107,261,117,513,441,105,509,265,437,121,109,266,507,435,122,110,264,508,436,120,108,268,505,433,124,112,269,506,434,125,113,123,267,504,432,111,675,679,684,680,415,305,311,631,571,416,309,632,572,303,414,304,310,630,570,301,418,307,634,574,302,419,308,635,575,300,417,306,633,573,317,296,629,413,569,294,315,627,411,567,295,316,628,412,568,299,313,625,409,565,297,314,626,410,566,408,298,312,624,564,683,681,674,682,0,43,217,607,71,2,218,608,69,44,1,42,216,606,70,46,4,220,610,67,47,5,221,611,68,45,3,219,609,66,215,41,605,7,77,39,213,603,8,75,40,214,604,6,76,37,211,601,10,73,38,212,602,11,74,9,36,210,600,72,692,689,686,688 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#47b26c2e0558f6c4fdff38c956d09d23d3aef780160b6fe0856dd3e8f07caf34, 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 16:54:03 · history