Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 6599da2fb819…

magma 6599da2fb819
Size
705
Isomorphism class hash
6599da2fb819a4667ee143d65c5491747aecdd8acb5b2eba6c5672f77ac1976d
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 17:39:19
Display reorder
660,135,597,473,549,65,136,598,63,474,550,134,596,64,472,548,138,600,61,476,552,139,601,62,477,553,137,599,60,475,551,479,133,603,71,555,131,604,69,480,556,132,602,70,478,554,606,129,67,482,558,607,130,68,483,559,605,128,66,481,557,666,669,671,662,609,291,220,297,335,610,292,336,218,298,608,290,337,219,296,612,294,334,223,300,613,295,332,221,301,611,293,333,222,299,215,615,289,341,303,616,287,342,216,304,614,288,343,217,302,285,618,340,214,306,286,619,338,212,307,284,617,339,213,305,685,686,687,691,537,163,417,173,75,538,161,76,418,174,536,162,77,416,175,540,159,74,420,172,541,160,72,421,170,539,158,73,419,171,423,543,154,81,164,544,152,82,424,165,542,153,83,422,166,157,546,80,426,167,155,547,78,427,168,156,545,79,425,169,665,672,664,668,585,369,485,344,234,586,370,235,486,345,584,368,233,484,346,588,372,230,488,347,589,373,231,489,348,587,371,232,487,349,491,591,375,225,350,592,376,226,492,351,590,374,224,490,352,378,594,228,494,353,379,595,229,495,354,377,593,227,493,355,678,674,675,681,357,561,381,517,237,358,562,238,382,518,356,560,236,380,516,360,564,240,384,520,361,565,241,385,521,359,563,239,383,519,387,363,567,243,523,364,568,244,388,524,362,566,242,386,522,570,366,246,390,526,571,367,247,391,527,569,365,245,389,525,663,667,670,661,150,621,449,505,21,151,622,22,450,506,149,620,23,448,504,146,624,20,452,508,147,625,18,453,509,148,623,19,451,507,455,141,627,12,511,142,628,13,456,512,140,626,14,454,510,630,144,15,458,514,631,145,16,459,515,629,143,17,457,513,696,698,700,697,498,99,529,429,104,499,100,105,530,430,497,98,106,528,428,501,102,107,532,432,502,103,108,533,433,500,101,109,531,431,535,496,97,110,435,647,645,111,646,644,503,96,112,534,434,653,654,113,655,652,657,658,114,659,656,649,650,115,651,648,704,702,701,703,437,38,31,8,251,438,36,252,32,6,436,37,253,30,7,440,41,250,34,11,441,39,248,35,9,439,40,249,33,10,29,443,44,257,3,444,42,258,27,4,442,43,259,28,5,47,446,256,25,2,45,447,254,26,1,46,445,255,24,0,699,694,693,695,207,399,125,405,58,208,400,59,126,406,206,398,57,127,404,210,402,54,124,408,211,403,55,122,409,209,401,56,123,407,116,205,397,49,411,203,395,50,117,412,204,396,48,118,410,393,201,52,119,414,394,202,53,120,415,392,200,51,121,413,680,676,679,684,283,461,271,633,324,281,462,325,269,634,282,460,323,270,632,279,464,320,267,636,280,465,321,268,637,278,463,322,266,635,262,274,467,330,639,272,468,331,260,640,273,466,329,261,638,470,277,326,265,642,471,275,327,263,643,469,276,328,264,641,682,683,677,673,312,185,573,197,84,313,186,85,574,198,311,187,86,572,199,308,184,87,576,196,309,182,88,577,194,310,183,89,575,195,579,318,176,90,188,319,177,91,580,189,317,178,92,578,190,179,314,93,582,191,180,315,94,583,192,181,316,95,581,193,689,692,688,690 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#5c1fa523b4d9d2fbb415708ccaff34546079d57eeb66e712dcba93d7172179c8, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 17:39:19 · history