Equation 677 Database

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Magma f84344121c31…

magma f84344121c31
Size
705
Isomorphism class hash
f84344121c318b38d8e3788a31ebf4dbdb175d7f8cbe3a1b6c93842b1fbf286a
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 21:49:56
Display reorder
660,413,412,411,408,409,410,418,419,417,414,415,416,101,99,100,97,98,96,107,105,106,103,104,102,351,352,353,350,348,349,357,358,359,356,354,355,194,192,193,197,195,196,200,198,199,203,201,202,71,69,70,67,68,66,62,60,61,65,63,64,671,679,682,686,483,485,484,481,482,480,491,489,490,487,488,486,40,41,39,36,37,38,46,47,45,42,43,44,531,532,533,530,528,529,537,538,539,536,534,535,543,544,545,542,540,541,549,550,551,548,546,547,601,602,600,604,605,603,607,608,606,610,611,609,661,669,666,670,454,453,455,452,450,451,444,445,446,447,448,449,565,566,564,568,569,567,571,572,570,574,575,573,290,288,289,293,291,292,296,294,295,299,297,298,635,633,634,631,632,630,626,624,625,629,627,628,17,15,16,13,14,12,23,21,22,19,20,18,674,677,680,685,86,85,84,88,89,87,91,92,90,94,95,93,397,398,396,400,401,399,403,404,402,406,407,405,273,274,275,272,270,271,264,265,266,267,268,269,117,118,119,116,114,115,108,109,110,111,112,113,173,171,172,169,170,168,179,177,178,175,176,174,697,700,702,704,506,505,504,508,509,507,511,512,510,514,515,513,638,636,637,641,639,640,644,642,643,647,645,646,458,456,457,461,459,460,464,462,463,467,465,466,187,188,186,190,191,189,185,183,184,181,182,180,577,578,576,580,581,579,583,584,582,586,587,585,689,693,694,695,331,330,332,333,334,335,328,329,327,324,325,326,342,343,344,345,346,347,340,341,339,336,337,338,306,307,308,309,310,311,304,305,303,300,301,302,320,318,319,323,321,322,315,316,317,314,312,313,32,30,31,35,33,34,27,28,29,26,24,25,663,665,667,676,283,282,284,285,286,287,280,281,279,276,277,278,493,494,492,496,497,495,499,500,498,502,503,501,623,621,622,619,620,618,614,612,613,617,615,616,133,134,132,136,137,135,139,140,138,142,143,141,552,553,554,555,556,557,558,559,560,561,562,563,688,691,692,696,478,477,479,476,474,475,468,469,470,471,472,473,525,526,527,524,522,523,516,517,518,519,520,521,49,50,48,52,53,51,55,56,54,58,59,57,656,654,655,659,657,658,651,652,653,650,648,649,588,589,590,591,592,593,594,595,596,597,598,599,675,690,683,684,223,222,224,225,226,227,220,221,219,216,217,218,435,436,437,434,432,433,441,442,443,440,438,439,120,121,122,123,124,125,126,127,128,129,130,131,373,374,372,376,377,375,379,380,378,382,383,381,144,145,146,147,148,149,150,151,152,153,154,155,698,699,701,703,229,228,230,231,232,233,234,235,236,237,238,239,241,242,240,244,245,243,247,248,246,250,251,249,392,390,391,395,393,394,387,388,389,386,384,385,157,158,156,160,161,159,163,164,162,166,167,165,254,252,253,257,255,256,260,258,259,263,261,262,662,664,668,673,0,1,2,3,4,5,6,7,8,9,10,11,209,207,208,205,206,204,215,213,214,211,212,210,361,362,360,364,365,363,367,368,366,370,371,369,76,77,75,72,73,74,82,83,81,78,79,80,421,422,420,424,425,423,427,428,426,430,431,429,672,678,681,687 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {63} 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 21:49:57 · history