Equation 677 Database

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Magma bc03fe2fbf8b…

magma bc03fe2fbf8b
Size
321
Isomorphism class hash
bc03fe2fbf8b60709ea2bb2c8bdb2b8e91b9d793d7a02b325129d771e57f237b
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 22:51:04
Display reorder
317,242,275,247,268,59,44,171,223,58,222,43,172,220,60,41,169,221,61,42,170,274,248,241,267,37,216,177,57,217,38,175,55,36,215,176,56,219,40,174,54,273,240,269,246,218,39,173,53,197,198,199,200,201,202,203,204,293,291,292,290,301,308,306,314,285,295,288,279,190,111,35,214,191,213,110,34,210,189,113,31,211,187,114,32,212,188,112,33,116,206,27,195,294,286,278,289,115,205,26,196,208,118,29,194,209,119,30,192,207,117,28,193,83,81,82,79,80,78,74,72,76,77,75,73,310,302,304,311,100,87,147,185,148,101,186,86,262,252,256,272,85,146,98,184,251,261,255,271,84,145,99,183,94,92,178,140,90,95,179,141,93,91,180,142,253,254,270,260,89,97,181,143,88,96,182,144,104,102,103,107,105,106,109,108,283,284,282,281,309,319,303,312,280,277,287,276,136,45,11,20,137,21,46,10,237,259,243,234,19,138,47,13,18,139,48,12,49,25,15,135,239,244,235,258,50,24,14,134,22,51,16,132,23,52,17,133,238,245,236,257,122,120,121,125,123,124,128,126,130,131,129,127,305,307,300,313,63,0,158,164,156,64,165,2,157,1,62,163,4,154,66,167,5,155,67,168,3,153,65,166,249,232,266,264,233,250,265,263,68,6,162,149,8,70,160,152,9,71,161,150,7,69,159,151,224,225,226,227,228,229,230,231,298,296,297,299,315,318,316,320 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#b8eeccb61bf3cf52a025c1a85426255b55158ec212ce139ae8ac4787df68c2e8, 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 22:51:05 · history