Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma b3058e28a20a…

magma b3058e28a20a
Size
381
Isomorphism class hash
b3058e28a20a3945234efeaf4e5bbbf9f99ad08035869722f4d633d39a205ed9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:32:25
Display reorder
380,275,271,280,285,290,295,24,19,20,21,22,23,302,303,304,305,301,300,26,27,28,29,30,25,260,265,241,246,251,255,216,221,225,230,235,211,200,205,181,186,190,195,161,166,171,176,150,155,35,36,37,38,39,40,32,33,143,147,34,31,16,15,17,18,13,14,342,344,365,338,361,340,359,377,345,372,279,274,284,289,293,298,120,115,116,117,118,119,322,323,318,319,320,321,122,123,124,125,126,121,263,268,244,249,253,258,218,223,228,233,238,213,204,209,183,188,193,199,163,168,173,178,153,158,130,131,132,133,134,135,127,128,129,6,145,149,138,137,139,140,141,136,339,330,369,352,364,353,356,379,354,373,276,270,281,286,291,296,72,73,74,75,76,71,316,317,312,313,314,315,79,80,81,82,77,78,261,266,240,245,250,256,215,220,226,231,236,210,201,206,180,185,191,196,160,165,170,175,151,156,86,87,88,83,84,85,8,9,10,11,12,7,90,89,91,92,142,146,349,331,366,343,362,348,358,376,332,370,278,273,283,288,294,299,2,3,4,5,1,0,328,329,324,325,326,327,113,114,109,110,111,112,264,269,243,248,254,259,219,224,229,234,239,214,203,208,184,189,194,198,164,169,174,179,154,159,100,101,102,103,104,99,98,93,94,95,96,97,105,108,144,148,106,107,350,337,368,333,363,351,355,378,336,374,277,272,282,287,292,297,55,56,57,58,53,54,309,310,311,306,307,308,64,59,60,61,62,63,262,267,242,247,252,257,217,222,227,232,237,212,202,207,182,187,192,197,162,167,172,177,152,157,44,45,46,41,42,43,67,68,69,70,65,66,48,47,49,50,51,52,347,334,367,335,360,341,357,375,346,371 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218, M = {73} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:32:25 · history