Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma a1a9251846fd…

magma a1a9251846fd
Size
381
Isomorphism class hash
a1a9251846fd3cbfd1301909d7235754ea47da058454cb4161e81ff8ff834479
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 23:46:35
Display reorder
380,34,33,35,30,31,32,241,245,250,255,260,265,22,23,18,19,20,21,296,270,275,280,286,291,24,25,26,27,28,29,15,16,17,12,13,14,322,323,318,319,320,321,170,175,151,156,160,165,190,195,200,205,181,185,8,9,10,11,6,7,225,215,230,235,211,220,343,339,342,374,341,366,361,340,355,376,116,115,117,118,119,114,243,248,253,258,263,268,101,96,97,98,99,100,298,273,278,283,288,294,110,111,112,113,108,109,92,93,94,95,90,91,312,313,314,315,316,317,173,178,153,158,163,168,193,198,203,208,183,188,104,105,106,107,102,103,228,218,233,238,213,223,336,349,351,372,350,368,363,332,358,378,72,77,73,74,75,76,242,247,252,257,262,267,5,1,0,2,3,4,297,272,277,282,287,292,69,70,71,66,67,68,80,81,82,83,78,79,325,326,327,328,329,324,171,176,150,155,161,166,191,196,201,206,180,186,87,88,89,84,85,86,226,216,231,236,210,221,338,346,331,370,348,365,360,347,356,375,133,132,134,135,136,137,244,249,254,259,264,269,146,147,148,149,144,145,299,274,279,284,289,293,131,126,127,128,129,130,142,143,138,139,140,141,301,300,302,303,304,305,174,179,154,159,164,169,194,199,204,209,184,189,120,121,122,123,124,125,229,219,234,239,214,224,354,334,333,373,335,369,364,353,359,379,54,59,55,56,57,58,240,246,251,256,261,266,38,39,40,41,36,37,295,271,276,281,285,290,51,52,53,48,49,50,62,63,64,65,60,61,307,308,309,310,311,306,172,177,152,157,162,167,192,197,202,207,182,187,43,44,45,46,47,42,227,217,232,237,212,222,344,330,352,371,345,367,362,337,357,377 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#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, M = {75} 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 23:46:36 · history