Equation 677 Database

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Magma 7ce033fb3cba…

magma 7ce033fb3cba
Size
321
Isomorphism class hash
7ce033fb3cbaa2e0733f8f41d06d5faa236f0be74cd11ea48aad8515452e59cd
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 22:27:28
Display reorder
316,255,275,251,270,115,125,199,223,116,222,126,200,127,114,220,201,128,113,221,202,256,250,274,271,108,216,203,129,109,217,204,130,110,215,205,131,219,111,206,132,273,249,272,257,218,112,207,133,157,155,156,160,158,159,153,154,287,288,286,289,303,305,308,312,281,295,284,279,146,68,58,214,147,213,69,59,67,145,210,56,65,143,211,57,66,144,212,55,151,4,51,60,285,276,278,280,152,3,50,61,1,150,54,62,0,148,52,63,2,149,53,64,80,81,79,83,84,82,86,87,88,89,90,85,310,307,306,313,49,77,96,141,97,48,142,78,244,242,239,260,47,99,76,140,238,245,241,259,46,98,75,139,95,70,134,43,93,71,135,41,94,72,136,42,240,243,258,237,73,92,137,44,74,91,138,45,7,5,6,10,8,9,208,209,293,291,292,294,301,319,304,314,283,282,290,277,196,122,33,104,195,105,121,34,254,269,248,234,124,198,106,35,123,197,107,36,194,102,37,120,268,247,235,253,193,103,38,119,101,191,39,117,100,192,40,118,246,267,236,252,23,21,22,26,24,25,29,27,31,32,30,28,309,300,302,311,166,15,175,185,176,167,186,16,177,17,165,184,169,178,18,181,170,179,19,182,168,180,20,183,263,232,265,262,264,233,266,261,174,11,190,164,13,171,187,162,14,172,188,163,12,173,189,161,224,225,226,227,228,229,230,231,298,296,297,299,317,315,318,320 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#35abc55380bad4d0eeaaa3ec3d1bddd8996633b3da151c70fe1eca862e930666, 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 22:27:29 · history