Equation 677 Database

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Magma 0844b1255fef…

magma 0844b1255fef
Size
321
Isomorphism class hash
0844b1255fef80281d53258d4861f9a80ab4fdad17ee30470dcbf339c437b8b1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:22:15
Display reorder
300,124,239,238,159,172,235,234,160,125,173,237,123,236,161,171,230,231,158,120,168,233,232,156,121,169,228,229,157,122,170,251,250,165,130,178,247,246,166,131,179,249,248,167,129,177,242,243,164,126,174,244,245,162,127,175,240,241,163,128,176,307,304,313,314,270,268,2,269,271,1,272,273,274,275,265,267,0,264,266,5,252,253,254,255,256,3,257,258,259,4,260,261,263,262,8,293,292,294,295,6,297,296,299,298,7,288,289,291,290,277,11,276,278,279,281,9,280,282,283,285,10,284,286,287,317,319,318,320,220,76,50,23,208,48,77,21,221,209,75,219,49,22,207,53,72,19,216,204,73,51,20,217,205,52,74,18,218,206,56,82,14,226,214,54,83,12,227,215,55,81,13,225,213,78,59,17,222,210,79,57,15,223,211,80,58,16,224,212,309,311,302,301,183,196,71,103,135,69,197,104,184,136,195,185,70,102,137,67,192,106,182,134,193,68,107,180,132,66,194,105,181,133,62,202,101,189,141,60,203,99,190,142,61,201,100,191,143,198,65,97,188,140,199,63,98,186,138,200,64,96,187,139,315,305,316,308,112,41,91,26,148,92,39,24,113,149,40,111,90,25,147,94,37,29,108,144,38,95,27,109,145,93,36,28,110,146,89,47,32,118,154,87,45,30,119,155,88,46,31,117,153,43,85,35,114,150,44,86,33,115,151,42,84,34,116,152,306,303,312,310 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#1de75750e9587644a990145f0b96f270fc04381fd8036a009d6bb6ea07359c52, M = {60} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 21.

last edited by qawbecrdtey at 2026-10-01 22:22:16 · history