Equation 677 Database

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Magma 382ba1c7de37…

magma 382ba1c7de37
Size
321
Isomorphism class hash
382ba1c7de373202ecaba010ecf787bf116a81fd15deba0abfef7f12a129d937
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 23:04:24
Display reorder
313,245,252,275,233,63,89,15,223,64,90,16,222,62,92,220,17,61,91,221,18,244,253,234,274,95,56,216,13,93,57,14,217,58,94,12,215,59,97,219,10,254,243,232,273,96,60,11,218,189,190,188,185,186,187,191,192,291,289,290,292,305,304,308,317,294,276,288,278,205,3,23,120,206,4,22,121,209,0,124,19,207,2,122,20,208,1,21,123,8,211,118,28,277,295,279,287,210,9,27,119,214,7,117,24,5,212,25,115,6,213,26,116,184,182,183,180,181,179,175,173,177,178,176,174,310,302,300,315,161,29,170,107,160,30,106,169,268,235,258,271,163,31,172,109,269,236,272,259,162,32,108,171,33,157,166,112,34,158,110,167,159,35,111,168,267,237,270,260,36,155,113,164,37,156,114,165,78,76,77,74,75,73,80,79,282,293,284,283,303,319,306,316,281,285,280,286,71,86,100,48,72,85,101,49,248,251,240,255,69,88,50,98,70,87,99,51,84,65,52,104,250,246,257,241,66,83,105,53,67,81,54,103,82,68,102,55,249,247,256,242,195,193,194,198,196,197,201,199,203,204,202,200,307,309,301,318,133,151,45,139,134,149,140,46,132,150,141,47,129,154,44,142,130,152,42,143,131,153,144,43,265,261,238,263,266,262,264,239,125,148,138,38,127,147,39,135,145,128,136,40,146,126,137,41,224,225,226,227,228,229,230,231,298,296,297,299,311,314,312,320 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#f8838644c69f7fdfa74529bfff2a78ed4214bd0b4502e0a1aafa31f9fac0d26b, 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 23:04:24 · history