Equation 677 Database

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Magma 4c16cf502c19…

magma 4c16cf502c19
Size
720
Isomorphism class hash
4c16cf502c19665f7ee39db9317eb945bb91cf61a8afc0d2245000890a476aa7
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 719) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 13:29:55
Display reorder
13,14,1,0,2,3,4,5,6,7,8,9,10,11,12,719,196,194,158,197,180,159,198,181,160,199,182,161,200,183,162,201,184,163,202,185,164,203,186,150,204,187,151,205,188,152,206,189,153,207,190,154,208,191,155,209,192,156,195,193,157,175,167,168,169,170,171,172,173,174,177,178,179,165,166,176,690,688,687,689,535,572,553,536,573,554,537,574,540,538,575,541,539,576,542,525,577,543,526,578,544,527,579,545,528,580,546,529,581,547,530,582,548,531,583,549,532,584,550,533,570,551,534,571,552,569,561,562,563,564,565,566,567,568,556,557,558,559,560,555,681,682,679,680,239,223,242,225,224,243,226,210,244,227,211,245,228,212,246,229,213,247,230,214,248,231,215,249,232,216,250,233,217,251,234,218,252,235,219,253,236,220,254,237,221,240,238,222,241,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,700,702,701,699,63,47,79,64,48,80,65,49,81,66,50,82,67,51,83,68,52,84,69,53,85,70,54,86,71,55,87,72,56,88,73,57,89,74,58,75,60,59,76,61,45,77,62,46,78,43,35,36,37,38,39,40,41,42,30,31,32,33,34,44,716,717,718,715,414,398,430,415,399,431,416,400,432,417,401,433,418,402,434,419,403,420,405,404,421,406,390,422,407,391,423,408,392,424,409,393,425,410,394,426,411,395,427,412,396,428,413,397,429,379,386,387,388,389,375,376,377,378,381,382,383,384,385,380,704,706,705,703,320,369,336,321,370,337,322,371,338,323,372,339,324,373,340,325,374,341,326,360,342,327,361,343,328,362,344,329,363,330,315,364,331,316,365,332,317,366,333,318,367,334,319,368,335,351,358,359,345,346,347,348,349,350,353,354,355,356,357,352,678,676,675,677,477,461,493,478,462,494,479,463,480,465,464,481,466,450,482,467,451,483,468,452,484,469,453,485,470,454,486,471,455,487,472,456,488,473,457,489,474,458,490,475,459,491,476,460,492,443,435,436,437,438,439,440,441,442,445,446,447,448,449,444,709,708,707,710,264,314,281,265,300,282,266,301,283,267,302,284,268,303,270,269,304,271,255,305,272,256,306,273,257,307,274,258,308,275,259,309,276,260,310,277,261,311,278,262,312,279,263,313,280,297,289,290,291,292,293,294,295,296,299,285,286,287,288,298,696,698,697,695,515,497,15,516,498,16,517,499,17,518,500,18,519,501,19,520,502,20,521,503,21,522,504,22,523,505,23,524,506,24,510,507,25,511,508,26,512,509,27,513,495,28,514,496,29,655,647,648,649,650,651,652,653,654,657,658,659,645,646,656,712,713,711,714,598,633,600,599,634,601,585,635,602,586,636,603,587,637,604,588,638,605,589,639,606,590,640,607,591,641,608,592,642,609,593,643,610,594,644,611,595,630,612,596,631,613,597,632,614,615,622,623,624,625,626,627,628,629,617,618,619,620,621,616,685,684,683,686,141,125,92,142,126,93,143,127,94,144,128,95,145,129,96,146,130,97,147,131,98,148,132,99,149,133,100,135,134,101,136,120,102,137,121,103,138,122,104,139,123,90,140,124,91,108,115,116,117,118,119,105,106,107,110,111,112,113,114,109,691,693,694,692 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 720 = 16 + 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#82fda0c11d8b67dd90198c9d834359ac6146390672939dae5a097a0c09da5164, M = {0, 4, 8, 12, 16, 20, 24, 28, 33, 37, 41, 45, 49, 53, 57, 78} 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 2026-10-07 13:30:02 · history