Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma b6076f0ca4e1…

magma b6076f0ca4e1
Size
381
Isomorphism class hash
b6076f0ca4e1d37501949f2921320db1aaa14dfe6c10ad68eacfcce58e1ede2b
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 23:19:24
Display reorder
380,82,77,57,62,67,72,245,221,226,231,236,240,161,166,171,146,151,156,257,262,267,272,276,252,135,141,115,120,125,130,25,31,5,10,15,20,190,195,200,175,180,185,310,311,306,307,308,309,35,40,45,281,291,51,286,296,205,210,215,0,92,87,97,102,107,112,350,346,340,359,336,378,338,370,368,361,84,79,59,64,69,74,249,224,229,234,239,244,160,165,170,145,150,155,259,264,269,274,279,254,139,144,119,124,129,134,29,34,9,14,19,24,191,196,201,176,181,186,302,303,304,305,301,300,39,44,49,284,294,54,289,299,209,214,219,4,94,89,99,104,109,114,352,345,342,355,339,377,330,374,367,363,81,75,55,60,65,70,247,222,227,232,237,242,163,168,173,148,153,158,256,261,266,271,278,251,137,142,117,122,127,132,27,32,7,12,17,22,193,198,203,178,183,188,317,312,313,314,315,316,37,42,47,282,292,52,287,297,207,212,217,2,91,86,96,101,106,110,354,348,341,358,333,375,334,372,365,360,80,76,56,61,66,71,246,220,225,230,235,241,162,167,172,147,152,157,255,260,265,270,275,250,136,140,116,121,126,131,26,30,6,11,16,21,192,197,202,177,182,187,318,319,320,321,322,323,36,41,46,280,290,50,285,295,206,211,216,1,90,85,95,100,105,111,351,347,343,356,332,379,337,373,369,362,83,78,58,63,68,73,248,223,228,233,238,243,164,169,174,149,154,159,258,263,268,273,277,253,138,143,118,123,128,133,28,33,8,13,18,23,194,199,204,179,184,189,328,329,324,325,326,327,38,43,48,283,293,53,288,298,208,213,218,3,93,88,98,103,108,113,353,349,344,357,335,376,331,371,366,364 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#10cca86363523145d0eb290792d3d13154c9d146d7a7475a96ac2cf61ae39af6, M = {73} 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 23:19:25 · history