Equation 677 Database

← all  ·  ← by size  ·  ← size 399

Magma 6c1b1b40df52…

magma 6c1b1b40df52
Size
399
Isomorphism class hash
6c1b1b40df526e1a122d3aeebca6a93e0c6aec72c6c24f90c75a1f4d87cdae93
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 14:03:57
Display reorder
8,1,0,2,3,4,5,6,7,17,9,10,11,12,13,14,15,16,398,45,59,84,85,46,60,47,86,61,87,48,62,88,49,54,89,50,55,51,81,56,52,82,57,83,53,58,68,38,77,69,39,78,70,40,79,71,41,80,63,42,72,64,43,73,65,44,74,66,36,75,67,37,76,27,28,29,30,31,32,33,34,35,20,21,22,24,25,26,18,19,23,389,385,383,397,279,232,249,250,280,233,281,251,225,243,282,226,244,283,227,245,284,228,285,246,229,286,247,230,248,287,231,216,272,242,217,273,234,218,274,235,219,275,236,220,276,237,221,277,238,222,278,239,223,270,240,224,271,241,256,257,258,259,260,252,253,254,255,265,266,267,269,261,262,263,264,268,384,395,396,382,155,172,188,180,156,173,157,181,174,182,158,175,183,159,176,184,160,177,161,185,178,153,186,179,187,154,171,165,148,197,166,149,189,167,150,190,168,151,191,169,152,192,170,144,193,162,145,194,163,146,195,164,147,196,207,208,209,210,211,212,213,214,215,200,201,202,204,205,206,198,199,203,388,386,390,387,136,305,102,103,137,297,138,104,298,105,139,299,106,140,300,107,141,301,142,99,302,143,100,303,101,135,304,289,129,95,290,130,96,291,131,97,292,132,98,293,133,90,294,134,91,295,126,92,296,127,93,288,128,94,120,121,122,123,124,125,117,118,119,113,114,115,108,109,110,111,112,116,392,393,391,394,372,323,333,334,373,315,374,335,316,336,375,317,337,376,318,338,377,319,369,339,320,370,340,321,341,371,322,307,365,326,308,366,327,309,367,328,310,368,329,311,360,330,312,361,331,313,362,332,314,363,324,306,364,325,348,349,350,342,343,344,345,346,347,357,358,359,352,353,354,355,356,351,379,380,378,381 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#67934624b7e6297f1ed34cfee06fe7ed9249c169159cd974d367eb577f433812, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-08 14:04:00 · history