Equation 677 Database

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Magma 0802e4549e55…

magma 0802e4549e55
Size
321
Isomorphism class hash
0802e4549e554b2b82cd0299a4e885c6fff821253a51ba070a23fecd61402749
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 23:04:27
Display reorder
300,207,244,193,21,220,208,22,245,194,221,243,23,209,192,219,206,240,20,196,216,204,241,18,197,217,205,242,19,195,218,250,199,213,12,226,251,200,214,13,227,249,198,215,14,225,202,246,212,15,222,203,247,210,16,223,201,248,211,17,224,313,305,309,312,268,269,270,46,271,272,47,273,274,275,265,45,264,266,267,252,253,42,254,255,256,257,43,258,259,260,261,44,262,263,292,295,293,37,294,297,299,296,38,298,288,291,289,36,290,279,276,277,40,278,283,280,281,41,282,287,285,284,39,286,320,318,319,317,120,107,117,48,232,121,49,105,118,233,106,50,122,119,231,123,103,51,116,228,124,104,52,114,229,125,102,53,115,230,98,108,126,54,238,96,109,127,55,239,97,110,128,56,237,111,101,129,57,234,112,99,130,58,235,113,100,131,59,236,316,311,308,306,84,65,81,35,139,85,33,63,82,140,64,34,86,83,138,87,61,31,80,142,88,62,32,78,143,89,60,30,79,141,71,72,90,26,137,69,73,91,24,135,70,74,92,25,136,75,67,93,29,133,76,68,94,27,134,77,66,95,28,132,315,301,307,302,144,177,180,2,161,145,1,178,181,159,179,0,146,182,160,147,176,5,183,157,148,174,3,184,158,149,175,4,185,156,168,186,150,8,167,169,187,151,6,165,170,188,152,7,166,189,171,153,11,163,190,172,154,9,164,191,173,155,10,162,314,303,310,304 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#fb895e2582be84c8b2721db1499636a6dec5ebe66e3b80b47964e64d8130d57b, 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 23:04:28 · history