Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 882ecfd4dbdb…

magma 882ecfd4dbdb
Size
381
Isomorphism class hash
882ecfd4dbdb1f4d330e6dd7bb9432f27e3fe48ae0390efadc78cc9505752c37
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 23:33:44
Display reorder
380,271,295,276,281,286,294,114,115,116,112,113,239,107,108,109,110,111,106,135,136,137,138,139,140,145,146,141,142,143,144,149,150,151,152,147,148,39,40,35,36,37,38,133,134,129,130,131,132,46,41,42,43,44,45,302,303,304,305,301,300,267,262,242,247,252,257,349,371,355,375,353,339,338,354,348,352,270,296,275,280,285,290,128,123,124,125,126,127,117,118,119,120,121,122,20,21,22,19,1,237,215,216,217,218,213,214,222,223,224,219,220,221,187,188,183,184,185,186,13,14,15,16,17,18,178,179,180,181,182,177,313,314,315,316,317,312,265,260,241,245,250,255,351,374,366,376,334,360,361,367,350,335,272,297,277,282,287,291,225,226,227,228,229,230,234,235,236,231,232,233,51,52,47,48,49,50,6,0,2,3,4,5,8,9,10,11,12,7,199,200,195,196,197,198,57,58,53,54,55,56,190,191,192,193,194,189,325,326,327,328,329,324,266,261,240,246,251,256,369,370,333,377,331,362,363,365,368,340,273,298,278,283,288,292,168,169,170,165,166,167,176,171,172,173,174,175,154,155,156,157,158,153,66,67,68,69,238,65,61,62,63,64,59,60,210,211,212,207,208,209,164,159,160,161,162,163,205,206,201,202,203,204,311,306,307,308,309,310,268,263,243,248,253,258,358,372,341,378,356,330,364,342,359,357,274,299,279,284,289,293,94,95,96,97,98,99,103,104,105,100,101,102,87,82,83,84,85,86,27,28,23,24,25,26,31,32,33,34,29,30,70,71,72,73,74,75,89,90,91,92,93,88,78,79,80,81,76,77,318,319,320,321,322,323,269,264,244,249,254,259,347,373,337,379,332,344,343,336,346,345 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, M = {69} 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 23:33:45 · history