Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma ad19a24e71a1…

magma ad19a24e71a1
Size
705
Isomorphism class hash
ad19a24e71a15a7dd3853a3784e23d71ed63243b069907892792861a5ca6985e
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 15:16:46
Display reorder
660,253,83,422,379,423,254,425,81,424,380,82,421,252,420,378,429,256,79,428,382,431,257,80,430,383,427,255,78,426,381,74,259,418,419,377,72,260,414,415,375,73,258,416,417,376,262,77,411,410,373,263,75,412,413,374,261,76,409,408,372,666,664,668,665,301,208,463,226,198,302,199,209,464,227,207,200,300,462,225,201,304,204,466,222,202,305,205,467,223,203,303,206,465,224,214,307,196,461,217,215,308,197,459,218,213,306,195,460,216,310,210,192,457,220,311,211,193,458,221,309,212,194,456,219,688,686,685,687,98,495,343,353,63,96,64,496,344,351,494,65,97,342,352,62,101,498,346,349,60,99,499,347,350,61,100,497,345,348,493,104,69,341,359,491,102,70,339,357,492,103,71,340,358,107,489,68,337,355,105,490,66,338,356,106,488,67,336,354,663,662,670,669,313,483,451,233,439,314,440,484,452,231,482,438,312,450,232,442,316,486,454,229,443,317,487,455,230,441,315,485,453,228,481,319,437,449,239,479,320,435,447,237,480,318,436,448,238,322,477,433,445,235,323,478,434,446,236,321,476,432,444,234,675,673,677,674,58,587,271,331,586,59,588,589,272,332,585,584,57,270,330,592,54,593,274,334,594,55,595,275,335,590,56,591,273,333,582,49,583,269,329,578,50,579,267,327,580,48,581,268,328,52,574,575,265,325,53,576,577,266,326,51,572,573,264,324,667,661,671,672,86,391,562,563,403,84,404,392,565,564,390,402,85,560,561,406,89,394,568,569,407,87,395,570,571,405,88,393,566,567,389,92,401,558,559,387,90,399,554,555,388,91,400,556,557,95,385,397,550,551,93,386,398,552,553,94,384,396,548,549,697,698,694,695,17,515,475,0,8,15,646,647,644,645,523,522,16,474,1,654,13,655,652,653,658,14,659,656,657,650,12,651,648,649,520,23,521,473,7,517,21,516,471,5,518,22,519,472,6,19,512,11,469,3,20,513,9,470,4,18,514,10,468,2,702,701,703,704,153,166,635,634,277,154,278,167,636,637,165,276,155,633,632,280,152,162,641,640,281,150,163,642,643,279,151,164,639,638,157,144,283,630,631,158,145,284,626,627,156,146,282,628,629,147,160,286,622,623,148,161,287,625,624,149,159,285,620,621,699,700,693,696,44,611,539,538,610,42,612,613,541,540,608,609,43,537,536,617,47,616,545,544,618,45,619,547,546,615,46,614,543,542,606,39,607,534,535,603,40,602,531,530,605,41,604,532,533,38,598,599,526,527,36,600,601,528,529,37,597,596,524,525,680,679,683,684,292,171,32,182,507,293,508,172,30,180,173,506,291,31,181,510,288,170,35,185,511,289,168,33,183,509,290,169,34,184,177,298,505,27,188,178,299,503,28,186,179,297,504,29,187,294,176,501,26,191,295,174,502,24,189,296,175,500,25,190,681,682,676,678,364,248,131,108,137,365,135,246,129,109,247,136,363,130,110,133,360,251,127,111,134,361,249,128,112,132,362,250,126,113,243,370,143,122,114,244,371,141,120,115,245,369,142,121,116,366,242,139,125,117,367,240,140,123,118,368,241,138,124,119,690,689,691,692 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#0f0ec421cc32f9c063215c008f5f1d2db6033828d1c93d9b7da541d2d3cf51f3, 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 15:16:49 · history