Equation 677 Database

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Magma 42544d229d13…

magma 42544d229d13
Size
321
Isomorphism class hash
42544d229d13abaf606c62180a135a188f1e28906ec14413031a0582af8caf68
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 22:45:46
Display reorder
300,54,122,146,176,167,55,120,147,177,165,56,121,148,178,166,53,118,149,175,163,51,119,150,173,164,52,232,234,174,162,151,90,45,168,159,152,91,46,169,157,153,92,47,170,158,93,154,48,171,161,94,155,49,172,160,95,156,50,236,235,307,304,314,303,246,295,294,292,293,247,298,299,296,297,248,290,291,289,288,249,279,278,276,277,250,283,282,280,281,251,287,286,284,285,258,259,244,257,256,263,262,245,261,260,254,255,243,253,252,271,270,240,269,268,275,274,241,273,272,266,267,242,264,265,318,317,320,319,106,201,189,5,228,230,202,190,6,66,105,200,188,7,65,103,197,185,4,62,104,198,186,0,63,102,199,187,3,64,180,192,98,20,58,181,193,96,21,59,179,191,97,19,57,195,183,101,2,60,196,184,99,1,61,194,182,100,225,227,301,302,310,313,78,26,212,116,132,76,27,213,117,133,77,25,211,115,131,74,22,208,112,128,75,23,209,113,129,73,24,210,114,130,204,31,69,108,124,205,32,67,109,125,203,30,68,107,123,28,207,72,111,233,29,237,70,231,127,226,206,71,110,126,306,308,316,311,33,144,88,219,9,34,145,89,217,10,35,143,87,218,8,36,140,84,215,12,37,141,85,216,13,38,142,86,214,11,80,135,39,223,15,81,136,40,221,16,79,134,41,222,14,138,83,42,239,18,139,229,43,238,224,137,82,44,220,17,315,312,305,309 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#9a5b705888933f32bf6ccbec2fa43e8b7ad7ed280396865bc2fba9cb62c49c59, 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 22:45:47 · history