Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma fbcf55157bbf…

magma fbcf55157bbf
Size
705
Isomorphism class hash
fbcf55157bbff96526a78229aefa231027a89ec41e03aca0a667ffb7c3b164cb
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 15:32:00
Display reorder
660,424,384,332,396,410,330,385,397,425,408,386,423,331,398,409,335,387,399,420,413,388,333,400,421,411,334,389,401,422,412,338,390,402,430,416,336,391,403,431,414,337,392,404,429,415,393,341,405,426,419,394,339,406,427,417,395,340,407,428,418,685,686,688,687,237,251,185,500,225,183,249,498,238,226,250,239,184,499,227,188,254,503,240,228,252,186,501,241,229,187,253,502,242,230,180,257,495,243,231,181,255,496,244,232,182,256,497,245,233,260,179,494,246,234,258,177,492,247,235,259,178,493,248,236,701,702,704,703,68,379,623,325,23,621,380,326,66,21,378,67,622,324,22,619,382,328,71,19,383,620,329,69,20,618,381,327,70,18,614,377,323,63,14,612,375,321,64,12,613,376,322,65,13,373,617,319,62,17,374,615,320,60,15,372,616,318,61,16,670,669,672,671,268,128,194,510,75,192,126,511,269,76,127,267,193,512,77,190,124,513,271,74,125,191,514,272,72,189,123,515,270,73,200,119,508,266,81,198,117,509,264,82,199,118,507,265,83,122,196,504,262,80,120,197,505,263,78,121,195,506,261,79,680,677,679,678,201,215,517,58,279,518,213,59,202,280,214,203,516,57,281,520,218,54,204,282,216,521,55,205,283,519,217,56,206,284,523,221,49,207,277,524,219,50,208,278,522,220,48,209,276,224,526,52,210,273,222,527,53,211,274,223,525,51,212,275,689,690,691,692,586,592,300,100,571,301,593,101,587,572,591,585,302,99,570,299,588,96,582,574,589,297,97,583,575,298,590,98,584,573,306,598,106,577,569,307,599,107,578,567,308,597,105,576,568,594,305,102,580,565,595,303,103,581,566,596,304,104,579,564,697,698,700,699,11,31,647,631,46,645,32,632,10,47,30,6,646,630,45,643,34,634,8,42,35,644,635,9,43,642,33,633,7,44,638,29,629,5,37,636,27,627,3,38,637,28,628,4,36,25,641,625,0,40,26,639,626,2,41,24,640,624,1,39,661,662,664,663,439,151,135,157,348,136,152,158,440,349,150,438,137,156,350,138,147,153,442,351,148,139,154,443,352,140,149,155,441,353,133,142,163,437,346,134,143,164,435,347,132,141,162,436,345,145,129,159,433,342,146,130,160,434,343,144,131,161,432,344,682,681,684,683,371,314,608,116,357,606,312,114,369,358,313,370,607,115,359,611,317,112,367,360,315,609,113,368,361,610,316,111,366,362,603,652,653,655,654,604,656,657,659,658,605,649,648,650,651,311,602,110,365,356,309,600,108,363,354,310,601,109,364,355,693,694,696,695,534,551,84,554,294,85,549,552,535,295,550,536,86,553,296,87,547,557,537,293,548,88,555,538,291,89,546,556,539,292,90,542,560,532,285,91,540,558,533,286,92,541,559,531,287,545,93,563,528,288,543,94,561,529,289,544,95,562,530,290,666,665,668,667,477,481,166,447,461,167,482,448,478,459,480,479,165,449,460,169,484,446,476,457,485,170,444,474,458,168,483,445,475,456,172,487,453,468,467,173,488,454,469,465,171,486,455,470,466,490,175,452,471,463,491,176,450,472,464,489,174,451,473,462,674,673,676,675 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#1de75750e9587644a990145f0b96f270fc04381fd8036a009d6bb6ea07359c52, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 15:32:01 · history