Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma dc470c825eeb…

magma dc470c825eeb
Size
381
Isomorphism class hash
dc470c825eeb0ea98206ef03c29f0ff9b8aebbb5a83be20431b199ad4229e314
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 23:39:51
Display reorder
380,303,305,304,302,301,300,254,259,249,269,279,264,194,184,189,209,199,204,158,163,153,173,178,168,274,214,63,62,61,64,143,148,138,128,133,123,58,56,57,244,59,60,118,113,293,108,98,103,82,88,93,283,73,78,66,65,69,68,67,299,234,289,239,229,219,224,353,368,334,359,343,349,339,362,378,373,313,312,314,315,316,317,251,256,245,265,275,261,190,181,186,205,195,200,159,164,154,174,179,169,271,210,9,7,8,6,144,149,139,129,134,124,28,29,30,241,26,27,119,114,294,109,99,104,83,89,94,284,74,79,17,16,15,19,18,295,230,285,235,226,216,221,354,369,330,355,344,345,335,363,379,374,311,310,309,307,308,306,250,255,246,266,276,260,192,182,187,207,197,202,155,160,150,171,176,166,272,212,37,36,35,38,140,146,135,126,131,121,12,10,11,243,13,14,115,110,291,106,96,101,81,87,90,282,72,77,40,39,43,42,41,297,232,287,237,227,217,222,350,367,332,357,342,347,337,361,377,370,319,318,320,321,322,323,253,258,247,267,277,263,191,180,185,206,196,201,156,161,151,170,175,165,270,211,34,32,33,31,141,145,136,125,130,120,23,21,22,240,24,25,116,111,290,105,95,100,84,86,91,281,70,75,0,20,1,3,2,296,231,286,236,225,215,220,351,366,331,356,341,346,336,360,375,371,327,329,328,326,324,325,252,257,248,268,278,262,193,183,188,208,198,203,157,162,152,172,177,167,273,213,44,45,4,5,142,147,137,127,132,122,53,51,52,242,54,55,117,112,292,107,97,102,80,85,92,280,71,76,47,50,46,49,48,298,233,288,238,228,218,223,352,365,333,358,340,348,338,364,376,372 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#a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f, M = {74} 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 23:39:52 · history