Equation 677 Database

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Magma a5b2e2a07374…

magma a5b2e2a07374
Size
595
Isomorphism class hash
a5b2e2a07374b2c93f7b3b0309582d661b7e1dd41be0ddf7dca1064a889a5919
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-09 02:05:17
Display reorder
82,81,77,78,79,80,113,112,114,115,116,111,100,99,95,96,97,98,376,375,377,379,380,378,454,453,452,450,451,449,537,531,581,568,573,245,242,174,241,244,243,158,87,83,84,85,86,5,4,0,1,2,3,28,27,29,181,182,153,203,202,204,160,101,102,137,136,138,139,140,230,171,231,234,232,233,170,189,193,190,155,191,192,349,348,350,345,346,347,307,309,308,312,310,311,496,495,494,503,493,492,424,423,425,426,427,428,264,263,262,261,258,260,369,371,370,373,374,372,447,446,445,444,259,448,509,508,507,504,505,506,550,549,524,512,526,511,529,510,555,574,590,591,553,567,564,552,56,53,57,58,55,54,19,18,20,15,16,17,121,120,122,117,118,119,106,105,107,108,109,104,71,76,72,73,74,75,33,32,34,30,31,183,226,169,227,228,229,168,188,187,154,184,185,186,390,392,391,389,387,388,324,323,322,320,321,319,294,293,292,290,291,289,498,497,499,500,501,502,357,359,358,360,361,362,329,328,330,327,325,326,489,491,490,487,486,488,295,297,296,299,300,298,532,533,530,548,551,525,516,515,577,565,557,589,584,556,586,583,39,36,40,35,38,37,45,44,46,41,42,43,48,47,49,50,51,52,21,26,22,23,24,25,127,126,128,123,124,125,146,145,147,148,149,257,253,246,254,255,256,209,248,249,247,250,251,252,430,429,431,432,433,434,455,332,331,334,335,333,393,395,394,398,396,397,341,340,339,343,344,342,355,354,356,352,353,351,282,281,280,277,278,279,315,314,313,318,316,317,305,304,306,303,301,302,540,541,527,522,520,528,521,514,563,585,594,576,562,579,582,559,9,12,10,11,14,13,110,213,210,211,162,212,177,152,178,151,179,180,175,176,150,7,8,6,143,142,144,141,240,235,172,239,236,237,173,238,156,197,194,195,196,157,222,221,218,165,219,220,288,287,286,284,285,283,440,439,438,442,443,441,479,480,476,469,467,468,368,367,366,364,365,363,456,458,457,459,460,461,337,336,338,437,435,436,386,385,384,383,381,382,472,471,484,483,485,473,547,545,534,518,536,519,535,523,554,592,593,566,561,578,587,560,68,65,69,70,67,66,103,207,208,161,205,206,214,164,215,216,163,217,199,198,159,89,90,88,93,92,94,91,201,200,224,223,166,225,167,129,135,134,130,131,132,133,64,63,59,60,61,62,403,402,404,399,400,401,405,407,406,410,408,409,422,421,420,418,419,417,482,477,481,475,474,478,269,268,270,266,267,265,412,411,413,416,414,415,470,463,462,464,465,466,276,275,274,271,272,273,543,542,513,544,546,538,517,539,569,570,588,558,580,575,571,572 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#92768bb2ce71adf5f3645437d2daad1854a25afcd5bf6e7bdc519de5c37f97ae, M = the submagma generated by {6, 36} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-09 02:05:18 · history