Equation 677 Database

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Magma 025eae3edb3c…

magma 025eae3edb3c
Size
705
Isomorphism class hash
025eae3edb3cc70957c70e74d73be5f8c1691b83dc50c039f457a8fd7db7499d
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 16:27:16
Display reorder
660,43,501,514,502,511,44,521,534,522,531,42,481,494,482,491,46,434,420,422,431,448,453,47,449,452,45,461,462,471,474,622,634,620,41,631,642,654,641,39,651,602,614,600,40,611,556,542,540,37,553,38,576,562,560,573,596,582,581,36,593,696,686,694,693,270,509,512,513,500,268,529,532,533,520,269,489,492,493,480,273,432,429,433,421,457,458,271,459,443,272,469,473,460,472,633,632,629,265,621,653,652,649,266,640,613,612,609,267,601,554,555,549,264,541,262,574,575,569,561,594,595,589,263,580,685,687,688,697,23,410,170,374,314,21,411,171,375,315,22,409,172,373,313,19,169,406,370,310,407,167,20,371,311,18,408,372,312,168,380,176,416,14,320,381,177,417,12,321,379,178,415,13,319,175,376,412,17,316,15,173,377,413,317,174,378,414,16,318,667,680,673,662,113,231,221,350,242,111,229,222,351,243,112,230,220,349,241,109,224,227,346,238,228,225,110,347,239,108,226,348,240,223,356,219,237,119,248,357,217,235,117,249,355,218,236,118,247,215,352,233,115,244,116,216,353,234,245,214,354,232,114,246,661,674,671,676,181,503,504,516,515,179,523,524,536,535,180,483,484,496,495,184,424,423,436,435,444,445,182,447,446,183,463,476,475,464,636,624,623,187,635,656,644,643,185,655,616,604,603,186,615,544,558,543,190,557,188,564,578,563,577,584,598,583,189,597,700,703,701,692,32,517,518,519,508,30,537,538,539,528,31,497,498,499,488,35,438,437,439,428,440,441,33,442,450,34,478,479,468,477,639,637,638,27,628,657,659,658,28,648,619,617,618,29,608,552,559,551,26,548,24,572,579,571,568,592,599,591,25,588,704,690,695,691,97,505,506,507,510,98,525,526,527,530,96,485,486,487,490,100,426,425,427,430,454,455,101,456,451,99,465,467,470,466,627,626,625,103,630,647,646,645,104,650,607,606,605,102,610,546,547,545,106,550,107,566,567,565,570,586,587,585,105,590,689,698,702,699,154,128,278,326,134,152,126,279,327,135,153,127,277,325,133,150,274,131,322,137,129,275,151,323,138,149,130,324,136,276,332,284,123,145,132,333,285,124,143,419,331,283,125,144,139,280,328,122,148,140,146,281,329,120,141,282,330,121,147,142,681,683,668,664,4,81,62,386,84,5,82,60,387,85,3,83,61,385,86,1,65,80,382,87,78,63,0,383,88,2,79,384,89,64,392,68,72,10,90,393,66,73,11,91,391,67,74,9,92,71,388,75,6,93,7,69,389,76,94,70,390,77,8,95,678,663,684,670,259,54,398,302,163,260,55,399,303,161,261,56,397,301,162,258,394,57,298,166,58,395,256,299,164,257,59,300,165,396,308,404,52,250,158,309,405,53,251,159,307,403,51,252,160,400,304,48,253,157,254,401,305,49,155,402,306,50,255,156,677,675,666,679,199,338,205,362,290,197,339,206,363,291,198,337,204,361,289,202,208,334,358,286,335,209,200,359,287,201,336,360,288,207,368,203,344,194,296,369,418,345,195,297,367,210,343,196,295,212,364,340,193,292,191,213,365,341,293,211,366,342,192,294,665,669,672,682 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#3233330d12681148716a4d7ca0430e02a433d3f211b7945abf3bfa7e2eafe60e, 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 16:27:17 · history