Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma a37bb51f689e…

magma a37bb51f689e
Size
381
Isomorphism class hash
a37bb51f689eef0699d52e556e499a9131b3260f98215655580c0fb72579c36e
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 23:51:23
Display reorder
380,13,17,317,26,4,9,27,18,1,8,14,15,6,319,24,5,10,28,19,0,12,16,7,321,25,3,11,29,20,2,43,47,38,323,56,34,39,48,30,57,45,44,36,324,54,35,40,58,49,31,46,42,37,326,55,33,41,59,50,32,51,52,23,21,22,53,345,343,358,344,371,359,377,369,332,357,185,186,310,195,204,181,199,190,203,208,183,187,209,300,196,205,182,200,191,201,184,188,207,301,197,206,180,198,189,202,215,216,238,302,225,234,211,220,233,229,217,213,239,303,226,235,212,230,221,231,218,214,237,304,227,236,210,228,219,232,223,224,192,193,194,222,378,366,333,372,361,373,362,347,360,363,68,69,306,78,87,64,82,73,86,60,66,70,61,307,79,88,65,83,74,84,67,71,62,308,80,89,63,81,72,85,98,99,90,309,108,117,94,103,116,112,100,96,91,305,109,118,95,113,104,114,101,97,92,328,110,119,93,111,102,115,106,107,75,76,77,105,379,365,346,335,364,375,349,348,334,374,146,147,325,156,165,178,160,151,164,172,144,148,173,327,157,166,179,161,152,162,145,149,171,322,158,167,177,159,150,163,122,123,169,318,132,141,175,127,140,136,124,120,170,320,133,142,176,137,128,138,125,121,168,316,134,143,174,135,126,139,130,131,153,154,155,129,350,337,330,338,336,376,351,367,368,339,246,250,311,259,268,245,263,254,264,241,247,251,242,312,260,269,243,261,252,265,248,249,240,329,258,267,244,262,253,266,276,280,271,313,289,298,275,284,294,293,281,277,272,314,290,299,273,291,282,295,279,278,270,315,288,297,274,292,283,296,287,285,256,257,255,286,353,352,356,341,355,340,370,354,331,342 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#fbe9ed86dadd1d2d3ad6392c3ea8f135eb4c63ec1eafb4df5c2be2f85a75ce9e, M = {66} 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 23:51:24 · history