Equation 677 Database

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Magma e181ef7d58df…

magma e181ef7d58df
Size
381
Isomorphism class hash
e181ef7d58df6398aff026cbd1c120fc966fbb780916f17bc1ade50cec6b7e64
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:32:05
Display reorder
380,186,181,191,196,200,205,64,65,60,61,62,63,242,245,251,256,261,266,282,287,292,297,272,277,216,221,226,230,235,211,47,42,43,44,45,46,55,56,57,58,59,54,303,301,329,304,300,302,175,151,156,161,166,170,0,2,3,4,5,1,50,49,51,52,53,48,340,345,358,334,333,377,365,362,372,350,189,184,194,199,204,209,110,112,103,105,106,108,244,249,254,259,264,268,284,289,294,299,274,279,219,224,229,234,239,214,141,143,145,146,148,139,127,129,131,133,134,136,317,318,319,320,321,322,179,154,159,164,169,174,118,120,122,124,115,117,96,101,97,98,99,100,330,354,357,336,343,379,368,364,374,352,188,183,193,198,203,208,77,72,73,74,75,76,243,248,253,258,263,267,283,288,293,298,273,278,218,223,228,233,238,213,78,79,80,81,82,83,66,67,68,69,70,71,328,323,324,325,326,327,178,153,158,163,168,173,91,92,93,94,95,90,87,86,88,89,84,85,331,347,356,342,341,378,367,361,373,351,185,180,190,195,201,206,111,113,102,104,107,109,240,247,252,257,262,265,281,286,291,296,271,276,215,220,225,231,236,210,140,142,144,147,149,138,126,128,130,132,135,137,312,313,314,315,316,311,176,150,155,160,165,171,119,121,123,125,114,116,10,9,11,6,7,8,337,353,355,332,344,376,369,363,371,349,187,182,192,197,202,207,20,21,22,23,18,19,241,246,250,255,260,269,280,285,290,295,270,275,217,222,227,232,237,212,29,24,25,26,27,28,37,38,39,40,41,36,307,308,309,310,305,306,177,152,157,162,167,172,15,16,17,12,13,14,32,31,33,34,35,30,339,348,359,335,338,375,366,360,370,346 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218, M = {68} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:32:06 · history