Equation 677 Database

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Magma 17c3e361b4c5…

magma 17c3e361b4c5
Size
321
Isomorphism class hash
17c3e361b4c55c54399de47932bcff08acc6ebe1f78abde5a5323f9af5a5b16e
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 22:28:48
Display reorder
300,79,143,147,242,194,192,141,80,148,240,193,142,78,149,241,197,82,139,146,245,83,195,140,144,243,196,81,138,145,244,77,134,200,153,248,75,132,198,154,246,155,76,133,199,247,137,73,203,152,251,135,74,201,150,249,136,72,202,151,250,315,313,307,304,71,262,261,263,260,255,253,69,252,254,259,257,70,256,258,275,67,273,272,274,68,267,264,265,266,271,66,268,269,270,62,284,287,285,286,60,277,279,276,278,281,61,280,283,282,296,65,299,297,298,289,63,291,288,290,293,64,295,292,294,320,319,318,317,156,3,56,92,20,18,4,157,54,90,19,5,158,55,91,23,159,2,59,95,160,21,1,57,93,22,161,0,58,94,162,9,15,51,87,163,10,16,52,88,53,164,11,17,89,8,165,14,50,86,6,166,12,48,84,7,167,13,49,85,303,311,316,302,33,104,118,206,170,168,102,34,119,204,169,103,35,117,205,173,32,107,114,209,30,171,105,115,207,172,31,106,116,208,24,99,176,109,212,25,100,174,110,210,108,26,101,175,211,98,27,179,112,215,96,28,177,113,213,97,29,178,111,214,308,312,306,310,38,184,121,223,230,228,185,36,122,224,229,183,37,120,222,233,41,180,124,226,39,231,181,125,227,232,40,182,123,225,44,190,236,127,221,42,191,234,128,219,126,43,189,235,220,186,47,239,130,217,187,45,237,131,218,188,46,238,129,216,305,314,309,301 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#4af6d9f6d3730a7119657046629cd5cdd39170988afb99e43673591a2135edbf, 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 22:28:49 · history