Equation 677 Database

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Magma 8a2bc5c015c4…

magma 8a2bc5c015c4
Size
321
Isomorphism class hash
8a2bc5c015c4cfc21a81a9e3d782de3033d229152d0ef1720346557e833326dd
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 22:59:28
Display reorder
311,236,250,275,265,149,88,30,223,150,87,31,222,32,151,85,220,33,152,86,221,266,237,249,274,81,147,216,28,82,148,217,29,80,146,215,27,144,84,219,25,264,248,273,235,145,83,218,26,159,160,158,155,156,157,161,162,292,290,291,293,308,300,301,317,278,284,276,295,210,131,35,15,211,132,34,16,37,212,135,17,38,213,133,18,214,36,134,19,129,209,20,40,283,294,277,279,130,208,21,39,205,128,22,42,206,126,23,43,207,127,24,41,185,186,184,188,189,187,191,192,193,194,195,190,310,307,304,314,11,196,120,182,183,197,12,119,269,270,233,259,14,181,198,118,234,268,271,258,180,13,199,117,200,175,125,10,201,176,123,8,202,177,124,9,267,272,260,232,178,203,122,7,179,204,121,6,4,5,3,1,0,2,153,154,287,288,286,289,302,319,305,315,282,281,280,285,141,77,89,44,140,76,90,45,251,263,247,238,91,143,79,46,142,92,78,47,75,139,48,93,246,262,239,252,74,138,49,94,136,72,50,95,137,73,51,96,261,245,240,253,165,163,164,168,166,167,171,169,173,174,172,170,306,303,309,316,61,112,105,67,68,110,59,106,66,111,60,104,57,70,108,101,58,71,109,102,69,56,107,103,257,244,254,242,256,243,255,241,116,65,97,52,63,114,99,55,64,115,100,53,62,113,98,54,224,225,226,227,228,229,230,231,298,296,297,299,312,318,313,320 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#df8d5557b781bba61b7abe058eca13be711d66cc8eaff0dccefd52d205bc7b58, 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 22:59:29 · history