Equation 677 Database

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Magma 55bacb6ab6da…

magma 55bacb6ab6da
Size
705
Isomorphism class hash
55bacb6ab6da386be0d276b243ed34694f2f266b8d1f917eadaaaccc1bd8a5eb
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 15:05:17
Display reorder
660,209,376,4,340,424,207,374,5,338,422,208,375,3,339,423,205,379,1,343,427,206,377,0,341,425,204,378,2,342,426,200,371,10,335,419,198,372,11,336,420,199,373,9,337,421,370,203,6,334,418,368,201,7,332,416,369,202,8,333,417,676,678,677,682,257,161,320,304,400,258,159,321,302,398,259,160,322,303,399,256,157,323,307,403,254,158,324,305,401,255,156,325,306,402,248,167,326,299,395,249,165,327,300,396,250,166,328,301,397,163,251,329,298,394,164,252,330,296,392,162,253,331,297,393,663,667,671,669,221,268,281,564,488,219,266,282,562,486,220,267,283,563,487,217,271,280,567,491,218,269,278,565,489,216,270,279,566,490,212,263,272,559,483,210,264,273,560,484,211,265,274,561,485,262,215,275,558,482,260,213,276,556,480,261,214,277,557,481,687,681,673,684,631,630,183,634,633,615,614,181,618,617,623,622,182,626,625,655,654,179,658,657,639,638,180,642,641,647,646,178,650,649,591,590,174,594,593,599,598,172,602,601,607,606,173,610,609,582,583,177,585,584,184,234,175,552,467,185,235,176,553,466,704,699,702,703,96,113,54,436,512,97,111,55,434,510,98,112,56,435,511,99,109,57,439,515,100,110,58,437,513,101,108,59,438,514,102,119,52,431,507,103,117,53,432,508,104,118,51,433,509,115,105,48,430,506,116,106,49,428,504,114,107,50,429,505,690,691,689,693,352,388,223,68,292,350,386,224,66,290,351,387,222,67,291,355,391,226,71,295,353,389,227,69,293,354,390,225,70,294,347,383,229,63,287,348,384,230,64,288,349,385,228,65,289,382,346,232,62,286,380,344,233,60,284,381,345,231,61,285,661,662,666,664,122,134,440,536,146,120,132,441,534,144,121,133,442,535,145,125,137,443,539,149,123,135,444,537,147,124,136,445,538,148,128,140,446,531,152,126,138,447,532,150,127,139,448,533,151,143,131,449,530,155,141,129,450,528,153,142,130,451,529,154,692,695,696,694,89,462,42,476,576,87,460,43,474,574,88,461,44,475,575,85,465,45,479,579,86,463,46,477,577,84,464,47,478,578,95,457,40,471,571,93,458,41,472,572,94,459,39,473,573,456,91,36,470,570,454,92,37,468,568,455,90,38,469,569,680,688,679,675,635,632,316,629,628,619,616,314,612,613,627,624,315,620,621,659,656,319,652,653,643,640,317,636,637,651,648,318,644,645,595,592,311,589,588,603,600,312,596,597,611,608,313,604,605,586,587,310,581,580,453,554,308,171,169,452,555,309,168,170,700,698,697,701,364,24,247,412,500,362,25,245,410,498,363,26,246,411,499,367,27,243,415,503,365,28,244,413,501,366,29,242,414,502,359,30,238,407,495,360,31,236,408,496,361,32,237,409,497,33,358,241,406,494,34,356,239,404,492,35,357,240,405,493,668,670,672,665,524,77,17,193,548,522,75,15,194,546,523,76,16,192,547,527,73,13,196,551,525,74,14,197,549,526,72,12,195,550,519,83,23,191,543,520,81,21,189,544,521,82,22,190,545,79,518,19,187,542,80,516,20,188,540,78,517,18,186,541,674,685,686,683 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#02a5eb7a1dc0484d80c271e9dde4b7cc0db9de7edd8cff390e9bbef93843b6b3, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 15:05:18 · history