Equation 677 Database

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Magma ebd043e7afe6…

magma ebd043e7afe6
Size
321
Isomorphism class hash
ebd043e7afe6fdb9a5fd17e0a415fe9bfc4200583c106eea124e5108896943b2
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 22:27:36
Display reorder
300,225,104,248,10,236,249,105,226,11,237,224,106,9,238,250,103,221,247,6,235,101,222,245,7,233,102,223,246,8,234,239,216,0,95,227,240,217,2,96,228,241,215,1,97,229,219,242,4,98,230,220,243,5,99,231,218,244,3,100,232,303,302,311,315,290,289,291,32,288,294,292,295,33,293,299,296,34,297,298,284,286,287,31,285,277,278,279,29,276,280,282,283,30,281,255,254,251,252,253,258,259,24,256,257,263,262,25,260,261,267,266,26,265,264,271,270,27,269,268,275,274,28,272,273,318,320,317,319,50,153,164,41,70,165,154,51,42,68,52,152,43,69,166,149,49,163,44,66,150,47,161,45,67,151,48,162,46,65,155,56,39,144,61,156,57,40,145,59,157,58,38,143,60,55,158,35,147,64,53,159,36,148,62,54,160,37,146,63,301,316,314,306,140,14,176,110,81,177,12,141,111,82,142,13,112,80,178,17,139,175,109,77,15,137,173,107,78,16,138,174,108,79,167,131,116,20,72,168,132,117,18,73,169,133,118,19,71,134,170,115,23,75,135,171,113,21,76,136,172,114,22,74,310,305,313,308,182,203,122,84,202,123,204,183,85,200,184,205,83,201,124,206,181,121,87,198,207,179,119,88,199,208,180,120,86,197,128,188,90,209,193,129,189,91,210,191,130,190,89,211,192,187,127,93,212,196,185,125,94,213,194,186,126,92,214,195,307,304,312,309 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#37e131d0061e11ac6a08c1b5043c4a4bd1e23715ce44e1796d2c3958c15ae4cf, 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 22:27:37 · history