Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma d6dc8e8eca47…

magma d6dc8e8eca47
Size
381
Isomorphism class hash
d6dc8e8eca47c2e88d33803a9ed71de963949f73597dc81294584f9e7d5117f0
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 23:49:30
Display reorder
380,27,20,32,12,267,17,197,202,192,182,187,177,300,302,301,304,305,303,133,138,128,293,148,143,47,52,57,37,272,42,88,93,283,103,108,98,157,162,152,297,172,167,238,243,248,251,256,261,6,7,288,113,118,123,207,217,212,230,221,226,77,277,82,72,62,67,342,370,347,363,369,353,358,331,337,377,29,23,34,14,269,19,199,204,194,184,189,179,311,309,310,308,306,307,134,139,129,294,149,144,49,54,59,39,274,44,89,94,284,104,109,99,159,164,154,299,174,169,235,241,246,254,259,264,8,9,289,114,119,124,209,219,214,234,224,229,79,279,84,74,64,69,344,374,349,364,368,354,359,334,339,379,28,22,33,13,268,18,195,201,190,181,186,175,321,322,323,318,319,320,130,135,126,290,146,141,48,53,58,38,273,43,85,90,281,101,106,96,155,161,150,295,171,166,237,242,247,250,255,260,1,0,286,110,116,120,206,216,211,231,220,225,78,278,83,73,63,68,343,371,348,360,365,351,356,330,338,376,25,21,31,11,265,16,196,200,191,180,185,176,329,327,328,326,324,325,132,137,127,292,147,142,46,51,56,35,271,40,87,92,282,102,107,97,156,160,151,296,170,165,236,240,245,253,258,263,5,4,287,112,117,122,205,215,210,233,223,228,76,275,81,70,60,65,341,373,345,362,366,352,357,333,335,375,26,24,30,10,266,15,198,203,193,183,188,178,317,315,316,314,312,313,131,136,125,291,145,140,45,50,55,36,270,41,86,91,280,100,105,95,158,163,153,298,173,168,239,244,249,252,257,262,2,3,285,111,115,121,208,218,213,232,222,227,75,276,80,71,61,66,340,372,346,361,367,350,355,332,336,378 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, M = {68} 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 23:49:31 · history