Equation 677 Database

← all  ·  ← by size  ·  ← size 399

Magma 309d286fe934…

magma 309d286fe934
Size
399
Isomorphism class hash
309d286fe934b1b0e4a82a3015c804f401e8a040ae2b845da8638c03940b17b1
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 19:11:36
Display reorder
65,66,67,68,69,70,71,63,64,58,59,60,61,62,54,55,56,57,381,327,310,297,18,328,19,311,298,329,20,312,299,313,330,21,300,331,22,314,301,332,23,306,302,324,24,307,303,325,25,308,304,326,26,309,305,27,336,319,290,28,337,320,291,29,338,321,292,30,339,322,293,31,340,323,294,32,341,315,295,33,333,316,296,34,334,317,288,35,335,318,289,391,385,386,392,110,240,256,151,111,152,241,257,112,144,242,258,234,113,145,259,114,146,235,260,115,147,236,252,116,148,237,253,108,149,238,254,109,150,239,255,160,119,249,265,161,120,250,266,153,121,251,267,154,122,243,268,155,123,244,269,156,124,245,261,157,125,246,262,158,117,247,263,159,118,248,264,383,389,390,384,48,165,270,3,49,4,166,271,50,5,167,272,168,51,6,273,52,7,169,274,53,8,170,275,45,1,162,276,46,0,163,277,47,2,164,278,12,41,174,279,13,42,175,280,14,43,176,281,15,44,177,282,16,36,178,283,17,37,179,284,9,38,171,285,10,39,172,286,11,40,173,287,388,398,397,387,348,95,342,135,350,136,96,344,352,137,97,346,98,354,138,349,356,139,90,351,358,140,91,353,343,141,92,355,345,142,93,357,347,143,94,359,128,367,104,360,129,368,105,362,130,370,106,364,131,372,107,366,132,374,99,369,133,376,100,371,134,361,101,373,126,363,102,375,127,365,103,377,394,395,396,393,188,74,223,206,180,198,75,224,181,199,76,216,77,182,200,217,183,201,78,218,184,202,79,219,185,203,80,220,186,204,72,221,187,205,73,222,215,197,83,232,207,189,84,233,208,190,85,225,209,191,86,226,210,192,87,227,211,193,88,228,212,194,89,229,213,195,81,230,214,196,82,231,380,379,378,382 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#4a577c8f4e86eca7aaff11bca6efaa128e8b8d19eaca708b55c78b13d19097a6, 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 19:11:37 · history