Equation 677 Database

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Magma 851f85fa1699…

magma 851f85fa1699
Size
321
Isomorphism class hash
851f85fa1699cec4a744cd1b97e52201a0e2a58804920cc0798dd82ed6f0c1d0
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 22:33:06
Display reorder
300,44,201,111,82,101,42,202,112,83,99,203,81,43,113,100,47,200,110,78,97,198,45,108,79,98,46,199,109,80,96,117,39,192,73,107,118,40,193,74,105,119,41,194,72,106,38,116,195,76,103,36,114,196,77,104,37,115,197,75,102,304,303,309,305,251,288,291,290,289,249,292,295,294,293,297,298,250,299,296,247,285,287,286,284,276,248,279,278,277,246,281,283,282,280,255,242,252,254,253,259,240,256,258,257,263,241,261,262,260,245,267,264,266,265,243,271,268,270,269,244,275,273,274,272,317,318,320,319,21,131,189,168,62,22,129,190,169,60,130,170,23,191,61,20,127,188,171,65,128,18,186,172,63,19,126,187,173,64,180,12,122,174,68,181,13,120,175,66,182,14,121,176,67,15,183,125,177,71,16,184,123,178,69,17,185,124,179,70,302,301,315,316,53,135,213,165,144,51,136,214,166,145,137,167,52,215,146,49,134,212,164,147,132,50,210,162,148,48,133,211,163,149,204,59,141,156,150,205,57,142,157,151,206,58,143,158,152,55,207,140,159,153,56,208,138,160,154,54,209,139,161,155,308,306,307,310,29,235,4,91,234,27,237,5,92,236,238,90,28,3,239,25,232,1,94,233,229,26,0,95,228,24,231,2,93,230,10,35,217,89,216,11,33,219,87,218,9,34,221,88,220,31,6,222,85,223,32,7,224,86,225,30,8,227,84,226,314,312,311,313 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#5aa74a2d4b4bbe4036558963ef968fca94fa5f577bdbfbf2823cea2791e8d20b, 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 22:33:07 · history