Equation 677 Database

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Magma fc0632eabefb…

magma fc0632eabefb
Size
321
Isomorphism class hash
fc0632eabefba5396933dd36a9bc1764442adf60fc3334beb6732ccfdf612b75
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 22:54:41
Display reorder
314,255,264,232,275,88,131,6,223,89,130,7,222,87,128,8,220,86,129,9,221,254,263,233,274,81,124,10,216,82,125,11,217,83,123,12,215,127,84,13,219,262,253,234,273,85,126,14,218,48,49,50,51,52,53,54,55,277,278,279,276,303,300,307,318,292,294,287,284,171,205,161,122,172,206,162,121,170,209,165,118,168,207,163,119,169,208,164,120,176,211,159,114,293,295,286,283,177,210,160,113,214,175,158,116,212,173,156,117,174,213,157,115,194,195,193,197,198,196,200,201,202,203,204,199,310,302,305,317,191,112,16,71,192,111,15,72,272,261,235,249,190,110,18,69,271,260,236,248,189,109,17,70,184,106,21,65,185,104,19,66,186,105,20,64,259,270,237,247,107,187,22,68,188,108,23,67,98,99,100,101,102,103,166,167,290,288,289,291,301,319,304,316,280,285,281,282,58,132,77,95,59,133,78,94,244,265,252,258,57,134,79,97,56,135,80,96,63,136,75,93,246,266,251,257,62,137,76,92,138,60,74,90,139,61,73,91,245,267,250,256,0,2,1,4,5,3,182,183,180,178,179,181,306,308,309,315,44,147,31,151,42,148,32,152,43,149,33,150,47,146,30,154,45,144,28,155,46,145,29,153,242,268,240,238,243,269,241,239,41,140,37,24,141,40,36,26,142,38,34,27,39,143,35,25,224,225,226,227,228,229,230,231,298,296,297,299,313,311,312,320 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#bef86252e34aac6c2a18a1e8b323957fca09c4d4a3c476c0116e0c729e633257, 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 22:54:42 · history