Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 02aeb9ffc1ad…

magma 02aeb9ffc1ad
Size
381
Isomorphism class hash
02aeb9ffc1ad6daef129b2116d6b0b57162e1b98eb9973ad168d2d5a54bc73c8
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 23:40:21
Display reorder
380,65,216,60,52,57,46,15,293,14,12,13,233,112,227,117,97,102,107,253,258,263,238,243,248,298,280,286,275,266,273,147,137,143,134,121,126,170,175,165,156,161,151,181,186,190,196,201,206,80,77,70,222,92,87,40,211,36,28,32,20,307,308,306,310,309,311,367,360,331,336,345,378,358,352,371,340,67,217,62,50,55,47,1,291,0,2,3,230,110,226,115,96,101,105,250,256,260,235,241,246,295,282,288,278,268,272,146,136,140,130,122,127,172,177,167,157,162,152,182,187,192,197,202,207,81,75,72,221,90,85,42,212,37,25,30,22,319,320,318,322,321,323,366,362,332,337,346,375,355,351,372,342,68,218,63,53,58,48,10,292,11,8,9,232,113,228,118,98,103,108,252,257,262,237,242,247,297,283,285,276,265,270,145,135,141,132,123,128,173,178,168,155,160,150,183,188,193,198,203,208,83,78,73,223,93,88,43,213,38,26,31,23,300,302,301,304,303,305,365,363,333,338,347,377,357,353,373,343,66,215,61,51,56,45,7,290,6,4,5,231,111,225,116,95,100,106,251,255,261,236,240,245,296,281,287,277,267,271,148,138,142,131,120,125,171,176,166,158,163,153,180,185,191,195,200,205,82,76,71,220,91,86,41,210,35,27,33,21,312,313,314,315,317,316,368,361,330,335,349,376,356,350,370,341,69,219,64,54,59,49,19,294,18,16,17,234,114,229,119,99,104,109,254,259,264,239,244,249,299,284,289,279,269,274,149,139,144,133,124,129,174,179,169,159,164,154,184,189,194,199,204,209,84,79,74,224,94,89,44,214,39,29,34,24,329,327,328,326,325,324,369,364,334,339,348,379,359,354,374,344 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#b1a8d3ba3db58654b282150679ccf1b928926281c9ba708fe38c950723e6a1aa, M = {76} 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 23:40:22 · history