Equation 677 Database

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Magma fdd3022761d2…

magma fdd3022761d2
Size
705
Isomorphism class hash
fdd3022761d294ddc2340c608f4ea3db17af8de32ce96ec8156d6e55a66d888e
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 16:40:48
Display reorder
704,225,426,235,242,226,427,236,240,428,241,227,234,429,224,238,245,222,430,239,243,223,431,237,244,216,424,233,248,217,425,231,246,218,423,232,247,420,219,229,251,421,220,230,249,422,221,228,250,204,205,206,207,208,209,210,211,215,213,214,212,675,673,672,674,89,543,103,63,87,544,104,64,545,65,88,102,542,85,106,62,86,540,107,60,84,541,105,61,95,549,101,69,93,550,99,70,94,551,100,71,548,91,97,68,546,92,98,66,547,90,96,67,73,74,72,76,77,75,79,80,81,82,83,78,664,666,667,665,254,0,273,284,252,2,274,282,1,283,253,275,4,257,272,287,255,5,270,285,256,3,271,286,260,7,264,279,258,8,265,280,259,6,266,281,10,263,267,278,11,261,268,276,9,262,269,277,648,649,650,651,652,653,654,655,658,656,657,659,684,686,687,685,139,110,146,167,140,108,144,165,109,166,138,145,113,142,149,163,143,111,147,164,141,112,148,162,137,116,152,158,135,114,150,156,136,115,151,157,119,133,155,161,117,134,153,159,118,132,154,160,130,131,129,126,127,128,121,122,123,124,125,120,701,703,702,700,626,433,647,602,624,434,645,600,432,601,625,646,436,629,643,605,627,437,644,603,628,435,642,604,632,439,638,608,630,440,636,606,631,438,637,607,442,635,641,611,443,633,639,609,441,634,640,610,176,174,175,179,177,178,171,172,169,170,168,173,690,691,689,688,367,19,331,336,368,20,332,337,18,338,366,330,22,370,334,339,371,23,335,340,369,21,333,341,365,17,329,342,363,15,327,343,364,16,328,344,13,361,325,345,14,362,326,346,12,360,324,347,351,352,353,350,348,349,357,358,355,356,354,359,662,661,660,663,449,188,463,469,447,186,464,470,187,468,448,462,191,445,466,472,446,189,467,473,444,190,465,471,455,183,461,475,453,184,459,476,454,185,460,474,182,451,457,478,180,452,458,479,181,450,456,477,491,489,490,487,488,486,482,480,484,485,483,481,694,693,692,695,311,198,316,612,309,199,317,613,200,614,310,315,201,307,312,615,308,202,313,616,306,203,314,617,302,196,322,618,300,197,323,619,301,195,321,620,192,305,318,621,193,303,319,622,194,304,320,623,288,289,290,291,292,293,294,295,299,297,298,296,682,683,680,681,514,48,520,530,515,49,521,528,50,529,513,519,51,510,516,533,511,52,517,531,512,53,518,532,505,54,526,536,506,55,527,534,504,56,525,535,57,508,522,539,58,509,523,537,59,507,524,538,494,492,493,497,495,496,500,498,502,503,501,499,696,698,697,699,595,41,556,564,596,39,557,565,40,566,594,555,37,598,552,567,599,38,553,568,597,36,554,569,593,47,562,570,591,45,563,571,592,46,561,572,43,589,558,573,44,590,559,574,42,588,560,575,579,580,581,578,576,577,585,586,583,584,582,587,671,668,669,670,382,33,387,397,383,34,388,398,35,396,381,389,32,378,386,400,379,30,384,401,380,31,385,399,373,24,393,403,374,25,394,404,372,26,395,402,27,376,392,406,28,377,390,407,29,375,391,405,418,419,417,414,415,416,409,410,411,412,413,408,676,678,679,677 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#38a4e23a99caaa7b44b0fde217361d7389ff59fad772c7ae239f5a60818fe03a, 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 16:40:49 · history