Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma a49f84659a95…

magma a49f84659a95
Size
705
Isomorphism class hash
a49f84659a95d3eb87112be67c05b780118f9343a2840bf901c547ef5d7380ed
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 17:29:02
Display reorder
660,83,287,528,330,480,288,478,81,526,328,479,286,82,527,329,79,290,483,531,333,80,291,481,529,331,78,289,482,530,332,74,293,486,534,325,72,294,484,532,326,73,292,485,533,327,296,77,489,537,324,535,297,75,487,322,295,76,488,536,323,672,664,661,669,64,378,384,1,151,376,152,65,382,0,150,377,63,383,2,60,381,154,387,3,61,379,155,385,4,62,380,153,386,5,70,373,149,390,6,71,374,147,388,7,69,375,148,389,8,372,66,145,393,9,391,370,67,146,10,371,68,144,392,11,689,685,688,687,115,516,247,564,19,514,20,116,248,562,18,515,114,249,563,118,519,22,246,567,119,517,23,244,565,117,518,21,245,566,113,522,17,238,570,111,520,15,239,568,112,521,16,240,569,525,109,13,241,573,242,523,110,14,571,524,108,12,243,572,668,663,671,665,54,419,432,173,160,420,161,55,430,171,159,418,56,431,172,57,422,156,435,169,58,423,157,433,170,59,421,158,434,168,52,425,166,438,179,53,426,167,436,177,51,424,165,437,178,428,48,162,441,175,439,429,49,163,176,427,50,164,440,174,680,679,673,676,181,492,451,540,456,490,454,182,452,538,455,491,180,453,539,184,495,459,450,543,185,493,457,448,541,183,494,458,449,542,187,498,462,442,546,188,496,460,443,544,186,497,461,444,545,501,190,465,445,549,446,499,191,463,547,500,189,464,447,548,667,666,670,662,405,345,304,504,319,343,320,403,305,502,321,344,404,306,503,401,341,318,307,507,402,342,316,308,505,400,340,317,309,506,396,336,310,302,510,394,334,311,303,508,395,335,312,301,509,339,399,313,298,513,299,337,397,314,511,338,398,315,300,512,696,695,694,693,41,620,623,622,621,614,615,39,613,612,617,616,40,619,618,37,632,633,635,634,38,625,624,627,626,36,629,628,631,630,47,644,645,647,646,45,637,636,639,638,46,640,641,643,642,656,43,657,659,658,651,649,44,648,650,652,42,653,655,654,702,703,701,704,94,219,588,206,195,217,196,95,586,207,197,218,93,587,208,90,215,194,591,205,91,216,192,589,203,92,214,193,590,204,85,225,201,594,212,86,223,202,592,213,84,224,200,593,211,221,88,610,597,611,595,222,89,198,209,220,87,199,596,210,697,700,699,698,285,468,360,600,552,466,550,283,358,598,551,467,284,359,599,281,471,555,363,603,282,469,553,361,601,280,470,554,362,602,276,474,558,366,606,274,472,556,364,604,275,473,557,365,605,477,279,561,369,609,367,475,277,559,607,476,278,560,368,608,678,682,684,674,137,576,408,101,228,574,226,135,406,99,227,575,136,407,100,133,579,231,411,97,134,577,229,409,98,132,578,230,410,96,143,582,234,414,107,141,580,232,412,105,142,581,233,413,106,585,139,237,417,103,415,583,140,235,104,584,138,236,416,102,683,681,677,675,25,122,348,266,261,120,259,26,346,267,260,121,24,347,265,28,125,257,351,262,29,123,258,349,263,27,124,256,350,264,31,128,252,354,272,32,126,250,352,273,30,127,251,353,271,131,34,255,357,268,355,129,35,253,269,130,33,254,356,270,690,691,692,686 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#57f0a2716884c2711bcb20a2573985b973a13e807353fc83680d5538f9af708e, 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 17:29:03 · history