Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma e2a305df0d0f…

magma e2a305df0d0f
Size
705
Isomorphism class hash
e2a305df0d0f61086ec49f01b8fab67c4cf9076bc7b57067d9dbe3231234ec41
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 16:44:48
Display reorder
660,280,441,71,355,84,82,439,278,72,353,83,440,279,70,354,80,283,437,67,351,281,81,438,68,352,282,79,436,69,350,286,447,90,77,361,445,88,78,284,359,446,89,76,285,360,86,443,73,289,357,444,87,74,287,358,85,442,75,288,356,675,685,679,686,11,19,195,49,202,203,20,9,193,50,204,21,10,194,51,201,7,22,198,52,8,199,23,196,53,6,200,24,197,54,2,25,208,190,47,26,209,191,1,48,27,210,192,0,46,207,28,189,5,43,29,205,187,3,44,206,30,188,4,45,671,672,665,669,297,92,374,460,558,556,93,298,372,458,557,91,296,373,459,554,300,95,370,456,301,555,96,371,457,299,553,94,369,455,295,98,564,380,466,99,562,378,293,464,97,563,379,294,465,560,101,376,291,462,102,561,377,292,463,559,100,375,290,461,680,676,677,683,38,228,453,615,407,405,229,39,451,613,406,227,37,452,614,410,41,224,449,618,42,408,225,450,616,40,409,226,448,617,36,655,654,656,659,639,638,640,34,643,647,646,648,35,651,620,621,622,32,624,631,630,632,33,635,411,223,454,31,619,704,700,699,702,65,417,570,242,484,482,415,66,568,243,483,416,64,569,244,480,61,413,566,245,62,481,414,567,246,63,479,412,565,247,56,423,490,576,248,421,488,574,57,249,422,489,575,55,250,486,419,572,59,251,420,487,573,60,252,485,418,571,58,253,689,694,690,692,218,335,496,107,515,513,336,219,494,108,514,337,217,495,106,511,221,334,492,103,222,512,332,493,104,220,510,333,491,105,216,326,521,502,113,327,519,500,214,114,328,520,501,215,112,517,329,498,212,109,330,518,499,213,110,516,331,497,211,111,661,664,668,666,140,167,261,429,527,525,168,141,262,427,526,166,139,260,428,523,143,163,264,425,144,524,164,265,426,142,522,165,263,424,146,173,533,259,435,174,531,257,147,433,172,532,258,145,434,529,169,255,149,431,170,530,256,150,432,528,171,254,148,430,691,695,696,693,271,319,594,152,306,307,317,269,592,153,305,318,270,593,151,302,267,315,590,155,268,303,316,591,156,266,304,314,589,154,277,325,312,600,158,323,313,598,275,159,324,311,599,276,157,308,321,596,273,161,322,309,597,274,162,310,320,595,272,160,681,687,673,674,178,548,367,508,13,14,546,179,365,506,15,547,180,366,507,16,177,551,363,504,175,17,549,364,505,176,18,550,362,503,184,658,652,653,657,642,636,637,185,641,650,644,645,186,649,625,627,626,183,623,634,628,629,181,633,12,552,368,182,509,701,697,703,698,238,582,386,472,539,537,580,236,384,470,538,581,237,385,471,535,241,578,382,468,239,536,579,383,469,240,534,577,381,467,233,588,545,392,478,586,543,390,234,476,587,544,391,235,477,541,584,388,232,474,585,542,389,230,475,540,583,387,231,473,663,662,670,667,345,118,398,128,606,604,119,346,396,129,605,120,344,397,127,602,348,117,394,131,349,603,115,395,132,347,601,116,393,130,343,124,612,404,134,125,610,402,341,135,126,611,403,342,133,608,123,400,339,137,121,609,401,340,138,607,122,399,338,136,684,678,682,688 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#3d4915088e45e024e7bce9a29cd7ec921add83e4b04ab0fb3d527eb1a5f02fc2, 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 16:44:49 · history